Deck 12: Hypothesis Testing for Two Populations

Question 1

A researcher wants to conduct a before/after study on 11 subjects to determine if a new cholesterol medication results in higher HDL cholesterol readings. The null hypothesis is that the average difference is zero while the alternative hypothesis is that the average difference is $\textbf{ not }$ zero. Scores are obtained on the subjects both before and after taking the medication. After subtracting the after scores from the before scores, the average difference is computed to be -2.40 with a sample standard deviation of 1.21. A 0.05 level of significance is selected. Assume that the differences are normally distributed in the population. The table t value for this test is ___.

A) 1.812
B) 2.228
C) 2.086
D) 2.262
E) 3.2467

Answer 1

2.228

Question 2

If the populations are normally distributed but the population variances are unknown the t statistic can be used as the basis for statistical inferences about the difference in two population means using two independent random samples.

Answer 2

True

Question 3

To determine if there is a difference in the speed of a wireless router from two different manufacturers, a network manager will draw independent samples of wireless routers from the two manufacturers and compare the difference in the sample means for the connection speed.

Answer 3

True

Question 4

A researcher is conducting a matched?pairs study. She gathers data on each pair in the study resulting in: Assume that the data are normally distributed in the population. The degrees of freedom in this problem are ___.

A) 4
B) 8
C) 5
D) 9
E) 3

Question 5

When testing for the difference between two population proportions, we use the "pooled" estimate of the proportion.

Question 6

If the populations are normally distributed and the variances of the two populations are equal, it is appropriate to use the "pooled" formula to determine the t statistic for the hypothesis test of the difference in the two population means.

Question 7

Sets of matched samples are also referred to as dependent samples.

Question 8

Hypothesis tests conducted on sets of matched samples are sometimes referred to as correlated t tests.

Question 9

If the populations are normally distributed but the population variances are unknown the z statistic can be used as the basis for statistical inferences about the difference in two population means using two independent random samples.

Question 10

If the variances of the two populations are $\textbf{ not }$ equal, it is appropriate to use the "pooled" formula to determine the t statistic for the hypothesis test of the difference in the two population means.

Question 11

The difference in two sample means is normally distributed for sample sizes ≥ 30, only if the populations are normally distributed.

Question 12

If the populations are normally distributed and the variances of the two populations are $\textbf{ not }$ equal, it is appropriate to use the "unpooled" formula to determine the t statistic for the hypothesis test of the difference in the two population means.

Question 13

A researcher wants to conduct a before/after study on 11 subjects to determine if a new cholesterol medication results in higher HDL cholesterol readings. The null hypothesis is that the average difference is zero while the alternative hypothesis is that the average difference is $\textbf{ not }$ zero. Scores are obtained on the subjects both before and after taking the medication. After subtracting the after scores from the before scores, the average difference is computed to be -2.40 with a sample standard deviation of 1.21. Assume that the differences are normally distributed in the population. The degrees of freedom for this test are ___.

A) 11
B) 10
C) 9
D) 20
E) 2

Question 14

In a set of matched samples, each data value in one sample is related to or matched with a corresponding data value in the other sample.

Question 15

A researcher wants to conduct a before/after study on 11 subjects to determine if a new cholesterol medication results in higher HDL cholesterol readings. The null hypothesis is that the average difference is zero while the alternative hypothesis is that the average difference is $\textbf{ not }$ zero. Scores are obtained on the subjects both before and after taking the medication. After subtracting the after scores from the before scores, the average difference is computed to be -2.40 with a sample standard deviation of 1.21. Assume that the differences are normally distributed in the population. The observed t value for this test is ___.

A) -21.82
B) -6.58
C) -2.4
D) 1.98
E) 2.33

Question 16

In conducting a matched-pairs hypothesis test, the null and alternative hypotheses always represent one-tailed tests.

Question 17

If the sample sizes are small, but the populations are normally distributed and the population variances are known, the z statistic can be used as the basis for statistical inferences about the difference in two population means using two independent random samples.

Question 18

A researcher is conducting a matched?pairs study. She gathers data on each pair in the study resulting in: Assume that the data are normally distributed in the population. The level of significance is selected to be 0.10. If a two-tailed test is performed, the null hypothesis would be rejected if the observed value of t is ___.

A) less than -1.533 or greater than 1.533
B) less than -2.132 or greater than 2.132
C) less than -2.776 or greater than 2.776
D) less than -1.860 or greater than 1.860
E) less than -2.000 or greater than 2.000

Question 19

A researcher is conducting a matched?pairs study. She gathers data on each pair in the study resulting in: Assume that the data are normally distributed in the population. The sample standard deviation (s_d) of the differences is ___.

A) 1.3
B) 1.14
C) 1.04
D) 1.02
E) 1.47

Question 20

If the sample sizes are greater than 30 and the population variances are known, the basis for statistical inferences about the difference in two population means using two independent random samples is the z statistic, regardless of the shapes of the population distributions.

Question 21

A researcher is interested in testing to determine if the mean price of a casual lunch is different in the city than it is in the suburbs. The null hypothesis is that there is no difference in the population means (i.e., the difference is zero). The alternative hypothesis is that there is a difference (i.e., the difference is $\textbf{ not }$ equal to zero). He randomly selects a sample of 9 lunch tickets from the city population resulting in a mean of $14.30 and a standard deviation of $3.40. He randomly selects a sample of 14 lunch tickets from the suburban population resulting in a mean of $11.80 and a standard deviation $2.90. He is using an alpha value of.10 to conduct this test. Assuming that the populations are normally distributed, the critical t value from the table is ___.

A) 1.323
B) 1.721
C) 1.717
D) 1.321
E) 2.321

Question 22

Golf course designer Roberto Langabeer is evaluating two sites, Palmetto Dunes and Ocean Greens, for his next golf course. He wants to prove that Palmetto Dunes residents (population 1) play golf more often than Ocean Greens residents (population 2). Roberto commissions a market survey to test this hypothesis. The market researcher used a random sample of 64 individuals from each suburb, and reported the following: ₁ = 15 times per month and
₂ = 14 times per month. Assume that $\sigma$ ₁ = 2 and $\sigma$ ₂ = 3. With $\alpha$ =.01, the critical z value is ___.

A) -1.96
B) 1.96
C) -2.33
D) -1.33
E) 2.33

Question 23

Golf course designer Roberto Langabeer is evaluating two sites, Palmetto Dunes and Ocean Greens, for his next golf course. He wants to prove that Palmetto Dunes residents (population 1) play golf more often than Ocean Greens residents (population 2). Roberto commissions a market survey to test this hypothesis. The market researcher used a random sample of 64 individuals from each suburb, and reported the following: ₁ = 15 times per month and
₂ = 14 times per month. Assume that $\sigma$ ₁ = 2 and $\sigma$ ₂ = 3. With $\alpha$ =.01, the observed z value is ___.

A) 2.22
B) 12.81
C) 4.92
D) 3.58
E) 1.96

Question 24

A researcher is estimating the average difference between two population means based on matched?pairs samples. She gathers data on each pair in the study resulting in: Assume that the data are normally distributed in the population. To obtain a 95% confidence interval, the table t value would be ___.

A) 2.132
B) 1.86
C) 2.306
D) 2.976
E) 2.776

Question 25

Lucy Baker is analyzing demographic characteristics of two television programs, American Idol (population 1) and 60 Minutes (population 2). Previous studies indicate no difference in the ages of the two audiences. (The mean age of each audience is the same.) Her staff randomly selected 100 people from each audience, and reported the following: ₁ = 43 years and
₂ = 45 years. Assume that $\sigma$ ₁ = 5 and $\sigma$ ₂ = 8. Assuming a two-tail test and $\alpha$ =.05, the observed z value is ___.

A) -2.12
B) -2.25
C) -5.58
D) -15.38
E) -20.68

Question 26

Lucy Baker is analyzing demographic characteristics of two television programs, American Idol (population 1) and 60 Minutes (population 2). Previous studies indicate no difference in the ages of the two audiences. (The mean age of each audience is the same.) Lucy plans to test this hypothesis using a random sample of 100 from each audience. Her alternate hypothesis is ___.

A) $\mu$ ₁ - $\mu$ ₂ ≤ 0
B) $\mu$ ₁ - $\mu$ ₂ ≥ 0
C) $\mu$ ₁ - $\mu$ ₂ = 0
D) $\mu$ ₁ - $\mu$ ₂ $\neq$
E) $\mu$ ₁ - $\mu$ ₂ = 1

Question 27

Golf course designer Roberto Langabeer is evaluating two sites, Palmetto Dunes and Ocean Greens, for his next golf course. He wants to prove that Palmetto Dunes residents (population 1) play golf more often than Ocean Greens residents (population 2). Roberto plans to test this hypothesis using a random sample of 81 individuals from each suburb. His null hypothesis is ___.

A)
B)
C)
D)
E)

Question 28

Golf course designer Roberto Langabeer is evaluating two sites, Palmetto Dunes and Ocean Greens, for his next golf course. He wants to prove that Palmetto Dunes residents (population 1) play golf more often than Ocean Greens residents (population 2). Roberto plans to test this hypothesis using a random sample of 81 individuals from each suburb. His null hypothesis is ___.

A)
B)
C)
D)
E)

Question 29

You are evaluating investing in a cognitive training company. For this reason, you want to determine whether users who complete at least 75% of the recommended daily training for two months show improved levels of reading comprehension and problem solving skills. You select a random sample of new users and get test scores for each participant in the sample. The test score is a composite of reading comprehension and problem solving skills. Two months later, you randomly select 15 users who have completed 75% or more of the recommended training for the last two months and have them take a test similar to the initial test. You are interested in determining whether the average test score before training is different than the average test score after training for this sample. The after-training average is 92.8, which is 2.7 points higher than the before-training average. The sample standard deviations of the differences is 1.2. You can assume that the differences are normally distributed in the population. The degrees of freedom for this test are ___.

A) 30
B) 29
C) 28
D) 15
E) 14

Question 30

Lucy Baker is analyzing demographic characteristics of two television programs, American Idol (population 1) and 60 Minutes (population 2). Previous studies indicate no difference in the ages of the two audiences. (The mean age of each audience is the same.) Lucy plans to test this hypothesis using a random sample of 100 from each audience. Her null hypothesis is ___.

A) $\mu$ ₁ - $\mu$ ₂ $\neq$ 0
B) $\mu$ ₁ - $\mu$ ₂ ≥ 0
C) $\mu$ ₁ - $\mu$ ₂ = 0
D) $\mu$ ₁ - $\mu$ ₂ ≤ 0
E) $\mu$ ₁ - $\mu$ ₂ ≤ 1

Question 31

Golf course designer Roberto Langabeer is evaluating two sites, Palmetto Dunes and Ocean Greens, for his next golf course. He wants to prove that Palmetto Dunes residents (population 1) play golf more often than Ocean Greens residents (population 2). Roberto commissions a market survey to test this hypothesis. The market researcher used a random sample of 64 individuals from each suburb, and reported the following: ₁ = 15 times per month and
₂ = 14 times per month. Assume that $\sigma$ ₁ = 2 and $\sigma$ ₂ = 3. With $\alpha$ =.01, the appropriate decision is ___.

A) reject the null hypothesis $\sigma$ ₁² < $\sigma$ ₂²
B) accept the alternate hypothesis $\mu$ _{1 -} $\mu$ ₂ > 0
C) reject the alternate hypothesis n₁ = n₂ = 64
D) fail to reject the null hypothesis $\mu$ ₁ - $\mu$ ₂ > 0
E) do nothing

Question 32

A researcher is interested in testing to determine if the mean price of a casual lunch is different in the city than it is in the suburbs. The null hypothesis is that there is no difference in the population means (i.e., the difference is zero). The alternative hypothesis is that there is a difference (i.e., the difference is $\textbf{ not }$ equal to zero). He randomly selects a sample of 9 lunch tickets from the city population resulting in a mean of $14.30 and a standard deviation of $3.40. He randomly selects a sample of 14 lunch tickets from the suburban population resulting in a mean of $11.80 and a standard deviation $2.90. He is using an alpha value of.10 to conduct this test. Assuming that the populations are normally distributed and that the population variances are approximately equal, the degrees of freedom for this problem are ___.

A) 23
B) 22
C) 21
D) 1
E) 2

Question 33

Lucy Baker is analyzing demographic characteristics of two television programs, American Idol (population 1) and 60 Minutes (population 2). Previous studies indicate no difference in the ages of the two audiences. (The mean age of each audience is the same.) Her staff randomly selected 100 people from each audience, and reported the following: ₁ = 43 years and
₂ = 45 years. Assume that $\sigma$ ₁ = 5 and $\sigma$ ₂ = 8. With a two-tail test and $\alpha$ =.05, the appropriate decision is ___.

A) do not reject the null hypothesis $\mu$ ₁ - $\mu$ ₂ = 0
B) reject the null hypothesis $\mu$ ₁ - $\mu$ ₂ ≥ 0
C) reject the null hypothesis $\mu$ ₁ - $\mu$ ₂ = 0
D) do not reject the null hypothesis $\mu$ ₁ - $\mu$ ₂ ≤ 0
E) do nothing

Question 34

A researcher is conducting a matched?pairs study. She gathers data on each pair in the study resulting in: Assume that the data are normally distributed in the population. The level of significance is selected to be 0.10. If the alternative hypothesis is that the average difference is greater than zero, the null hypothesis would be rejected if the observed value of t is ___.

A) greater than 1.533
B) less than -1.533
C) greater than 2.132
D) less than -2.132
E) equal to 2.333

Question 35

Lucy Baker is analyzing demographic characteristics of two television programs, American Idol (population 1) and 60 Minutes (population 2). Previous studies indicate no difference in the ages of the two audiences. (The mean age of each audience is the same.) Her staff randomly selected 100 people from each audience, and reported the following: ₁ = 43 years and
₂ = 45 years. Assume that $\sigma$ ₁ = 5 and $\sigma$ ₂ = 8. With a two-tail test and $\alpha$ =.05, the critical z values are ___.

A) -1.64 and 1.64
B) -1.96 and 1.96
C) -2.33 and 2.33
D) -2.58 and 2.58
E) -2.97 and 2.97

Question 36

Golf course designer Roberto Langabeer is evaluating two sites, Palmetto Dunes and Ocean Greens, for his next golf course. He wants to prove that Palmetto Dunes residents (population 1) play golf more often than Ocean Greens residents (population 2). Roberto commissions a market survey to test this hypothesis. The market researcher used a random sample of individuals from each suburb, and reported the following: ₁ = 16 times per month and
₂ = 14 times per month. Assume that $\sigma$ ₁ = 4 and $\sigma$ ₂ = 3. With $\alpha$ =.01, the appropriate decision is ___.

A) do nothing
B) reject the null hypothesis $\sigma$ ₁ < $\sigma$ ₂
C) accept the alternate hypothesis $\mu$ _{1 -} $\mu$ ₂ < 0
D) reject the alternate hypothesis n₁ = n₂ = 64
E) do not reject the null hypothesis $\mu$ ₁ - $\mu$ ₂ = 0

Question 37

You are evaluating investing in a cognitive training company. For this reason, you want to determine whether users who complete at least 75% of the recommended daily training for two months show improved levels of reading comprehension and problem solving skills. You select a random sample of new users and get test scores for each participant in the sample. The test score is a composite of reading comprehension and problem solving skills. Two months later, you randomly select 15 users who have completed 75% or more of the recommended training for the last two months and have them take a test similar to the initial test. You are interested in determining whether the average test score before training is different than the average test score after training for this sample. The after-training average is 92.8, which is 2.7 points higher than the before-training average. The sample standard deviations of the differences is 1.2. You can assume that the differences are normally distributed in the population. The observed t value for this test is ___.

A) 7.26
B) 8.71
C) 9.55
D) 9.81
E) 33.75

Question 38

Golf course designer Roberto Langabeer is evaluating two sites, Palmetto Dunes and Ocean Greens, for his next golf course. He wants to prove that Palmetto Dunes residents (population 1) play golf more often than Ocean Greens residents (population 2). Roberto commissions a market survey to test this hypothesis. The market researcher used a random sample of 64 individuals from each suburb, and reported the following: ₁ = 16 times per month and
₂ = 14 times per month. Assume that $\sigma$ ₁ = 4 and $\sigma$ ₂ = 3. With $\alpha$ =.01, the observed z value is ___.

A) 18.29
B) 6.05
C) 5.12
D) 3.40
E) 3.20

Question 39

A researcher is estimating the average difference between two population means based on matched?pairs samples. She gathers data on each pair in the study resulting in: Assume that the data are normally distributed in the population. To obtain a 90% confidence interval, the table t value would be ___.

A) 1.86
B) 1.397
C) 1.533
D) 2.132
E) 3.346

Question 40

You are evaluating investing in a cognitive training company. For this reason, you want to determine whether users who complete at least 75% of the recommended daily training for two months show improved levels of reading comprehension and problem solving skills. You select a random sample of new users and get test scores for each participant in the sample. The test score is a composite of reading comprehension and problem solving skills. Two months later, you randomly select 15 users who have completed 75% or more of the recommended training for the last two months and have them take a test similar to the initial test. You are interested in determining whether the average test score before training is different than the average test score after training for this sample. The after-training average is 92.8, which is 2.7 points higher than the before-training average. The sample standard deviations of the differences is 1.2. You use a significance level of 0.10, and you can assume that the differences are normally distributed in the population. The table t value for this test is ___.

A) 1.761
B) 1.746
C) 1.753
D) 1.345
E) 1.339

Question 41

Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies, is reviewing the order filling operations at her warehouses. Her goal is 100% of orders shipped within 24 hours. In previous years, neither warehouse has achieved the goal, but the East Coast Warehouse has consistently out-performed the West Coast Warehouse. Her staff randomly selected 200 orders from the West Coast Warehouse (population 1) and 400 orders from the East Coast Warehouse (population 2), and reports that 190 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 356 orders within 24 hours. Assuming $\alpha$ = 0.05, the appropriate decision is ___.

A) reject the null hypothesis π₁ - π₂ = 0
B) reject the null hypothesis $\mu$ ₁ - $\mu$ ₂ ≤ 0
C) do not reject the null hypothesis $\mu$ ₁ - $\mu$ ₂ = 0
D) do not reject the null hypothesis π₁ - π₂ = 0
E) do not reject the null hypothesis π₁ - π₂ ≥ 0

Question 42

Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies, is reviewing the order filling operations at her warehouses. Her goal is 100% of orders shipped within 24 hours. In previous years, neither warehouse has achieved the goal, but the East Coast Warehouse has consistently out-performed the West Coast Warehouse. Her staff randomly selected 200 orders from the West Coast Warehouse (population 1) and 400 orders from the East Coast Warehouse (population 2), and reports that 190 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 372 orders within 24 hours. Assuming $\alpha$ = 0.05, the critical z value is ___.

A) -1.96
B) -1.64
C) 1.64
D) 1.96
E) 2.33

Question 43

Your company is evaluating two cloud-based, secured data storage services. "Pie in the Sky," the newer service, claims its uploading and downloading speeds are faster than the older service, "Cloudy but Steady Skies." You need to make a decision based on published access times for both services at different times and for varying file sizes. Your alternative hypothesis is ___.

A) $\sigma$ ₁² < $\sigma$ ₂²
B) $\mu$ ₁ - $\mu$ ₂ < 0
C) π₁ - π₂ = 0
D) $\mu$ ₁ - $\mu$ ₂ = 0
E) s₁ - s₂ = 0

Question 44

Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies, is reviewing the order filling operations at her warehouses. Her goal is 100% of orders shipped within 24 hours. In previous years, neither warehouse has achieved the goal, but the East Coast Warehouse has consistently out-performed the West Coast Warehouse. Her staff randomly selected 200 orders from the West Coast Warehouse (population 1) and 400 orders from the East Coast Warehouse (population 2), and reports that 190 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 372 orders within 24 hours. Maureen's alternative hypothesis is ___.

A) π₁ - π₂ $\neq$ 0
B) $\mu$ ₁ - $\mu$ ₂ > 0
C) π₁ - π₂ > 0
D) $\mu$ ₁ - $\mu$ ₂ $\neq$ 0
E) $\mu$ ₁ - $\mu$ ₂ ≥ 0

Question 45

Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies, is reviewing the order filling operations at her warehouses. Her goal is 100% of orders shipped within 24 hours. In previous years, neither warehouse has achieved the goal, but the East Coast Warehouse has consistently out-performed the West Coast Warehouse. Her staff randomly selected 200 orders from the West Coast Warehouse (population 1) and 400 orders from the East Coast Warehouse (population 2), and reports that 190 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 356 orders within 24 hours. Assuming $\alpha$ = 0.05, the observed z value is ___.

A) -3.15
B) 2.42
C) 1.53
D) 0.95
E) 1.05

Question 46

A researcher wishes to determine the difference in two population means. To do this, she randomly samples 9 items from each population and computes a 90% confidence interval. The sample from the first population produces a mean of 780 with a standard deviation of 240. The sample from the second population produces a mean of 890 with a standard deviation of 280. Assume that the values are normally distributed in each population. The point estimate for the difference in the means of these two populations is ___.

A) -110
B) 40
C) -40
D) 0
E) 240

Question 47

A researcher believes a new diet should improve weight gain. To test his hypothesis a random sample of 10 people on the old diet and an independent random sample of 10 people on the new diet were selected. The selected people on the old diet gain an average of 5 pounds with a standard deviation of 2 pounds, while the average gain for selected people on the new diet was 8 pounds with a standard deviation of 1.5 pounds. Assume that the values are normally distributed in each population and that the population variances are approximately equal. Using = 0.05, the critical t value used from the table for this is ___.

A) -1.96
B) -1.645
C) -2.100
D) -3.79
E) -1.734

Question 48

Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies, is reviewing the order filling operations at her warehouses. Her goal is 100% of orders shipped within 24 hours. In previous years, neither warehouse has achieved the goal, but the East Coast Warehouse has consistently out-performed the West Coast Warehouse. Her staff randomly selected 200 orders from the West Coast Warehouse (population 1) and 400 orders from the East Coast Warehouse (population 2), and reports that 190 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 372 orders within 24 hours. Assuming $\alpha$ = 0.05, the observed z value is ___.

A) -3.15
B) 2.42
C) 1.53
D) 0.95
E) 1.08

Question 49

A researcher believes a new diet should improve weight gain. To test his hypothesis a random sample of 10 people on the old diet and an independent random sample of 10 people on the new diet were selected. The selected people on the old diet gain an average of 5 pounds with a standard deviation of 2 pounds, while the average gain for selected people on the new diet was 8 pounds with a standard deviation of 1.5 pounds. Assume that the values are normally distributed in each population and that the population variances are approximately equal. Using $\alpha$ = 0.05, the observed t value for this test is ___.

A) -1.96
B) -1.645
C) -2.100
D) -3.79
E) -1.734

Question 50

You are interested in determining the difference in two population means. You select a random sample of 8 items from the first population and 8 from the second population and then compute a 95% confidence interval. The sample from the first population has an average of 12.2 and a standard deviation of 0.8. The sample from the second population has an average of 11.7 and a standard deviation of 1.0. Assume that the values are normally distributed in each population. The point estimate for the difference in means of these two populations is ___.

A) −0.2
B) 0.2
C) 0.5
D) −0.5
E) 0.06

Question 51

Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies, is reviewing the order filling operations at her warehouses. Her goal is 100% of orders shipped within 24 hours. In previous years, neither warehouse has achieved the goal, but the East Coast Warehouse has consistently out-performed the West Coast Warehouse. Her staff randomly selected 200 orders from the West Coast Warehouse (population 1) and 400 orders from the East Coast Warehouse (population 2), and reports that 190 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 372 orders within 24 hours. Assuming $\alpha$ = 0.05, the appropriate decision is ___.

A) do not reject the null hypothesis $\mu$ ₁ - $\mu$ ₂ = 0
B) do not reject the null hypothesis π₁ - π₂ = 0
C) reject the null hypothesis $\mu$ ₁ - $\mu$ ₂ = 0
D) reject the null hypothesis p₁ - p₂ = 0
E) do not reject the null hypothesis π₁ - π₂ ≥ 0

Question 52

You are interested in determining whether the mean price of electricity offered by solar companies is different in the southern states than in the northern states. You select a random sample of 8 solar companies from the southern states and 11 from the northern states. For the southern states, the average price is 12.2 cents per kWh (kilowatt hour) and the standard deviation is 0.8 cents per kWh. For the northern states, the average and standard deviation are 11.7 and 1.0 cents per kWh respectively. If you use a significance level α = 0.10 and assuming the values are normally distributed in both populations, the critical t value is ___.

A) 1.330
B) 1.729
C) 1.734
D) 1.740
E) 1.747

Question 53

Your company is evaluating two cloud-based secured data storage services. "Pie in the Sky," the newer service, claims its uploading and downloading speeds are faster than the older service, "Cloudy but Steady Skies." You need to make a decision based on published access times for both services at different times and for varying file sizes. To make your decision, you purchase a statistical study, which indicates that average download time for Pie in the Sky is 0.77 sec. per MB and for Cloudy but Steady Skies is 0.84. Assume that n₁ = n₂ = 50, $\sigma$ ₁ = 0.2 and $\sigma$ ₂ = 0.3. With $\alpha$ =.05, the observed z value is ___.

A) -9.71
B) -1.37
C) -0.7
D) 1.37
E) 1.96

Question 54

Suppose that.06 of each of two populations possess a given characteristic. Samples of size 400 are randomly drawn from each population. The standard deviation for the sampling distribution of differences between the first sample proportion and the second sample proportion (used to calculate the z score) is ___.

A) 0.00300
B) 0.01679
C) 0.05640
D) 0.00014
E) 0.12000

Question 55

A researcher wishes to determine the difference in two population means. To do this, she randomly samples 9 items from each population and computes a 90% confidence interval. The sample from the first population produces a mean of 780 with a standard deviation of 240. The sample from the second population produces a mean of 890 with a standard deviation of 280. Assume that the values are normally distributed in each population and that the population variances are approximately equal. The critical t value used from the table for this is ___.

A) 1.860
B) 1.734
C) 1.746
D) 1.337
E) 2.342

Question 56

You are interested in determining the difference in two population means. You select a random sample of 8 items from the first population and 8 from the second population and then compute a 95% confidence interval. The sample from the first population has an average of 12.2 and a standard deviation of 0.8. The sample from the second population has an average of 11.7 and a standard deviation of 1.0. Assume that the values are normally distributed in each population and that the population variances are approximately equal. The corresponding critical t value is ___.

A) 1.753
B) 1.761
C) 2.120
D) 2.131
E) 2.145

Question 57

Your company is evaluating two cloud-based secured data storage services. "Pie in the Sky," the newer service, claims its uploading and downloading speeds are faster than the older service, "Cloudy but Steady Skies." You need to make a decision based on published access times for both services at different times and for varying file sizes. To make your decision, you purchase a statistical study, which indicates that average download time for Pie in the Sky is 0.77 sec. per MB and for Cloudy but Steady Skies is 0.84. Assume that $\sigma$ ₁ = 0.2 and $\sigma$ ₂ = 0.3. With $\alpha$ =.05, the critical z value is ___.

A) 1.645
B) -1.645
C) 1.96
D) -1.96
E) 2.33

Question 58

Suppose that.06 of each of two populations possess a given characteristic. Samples of size 400 are randomly drawn from each population. The probability that the difference between the first sample proportion which possess the given characteristic and the second sample proportion which possess the given characteristic being more than +.03 is ___.

A) 0.4943
B) 0.9943
C) 0.0367
D) 0.5057
E) 0.5700

Question 59

Your company is evaluating two cloud-based secured data storage services. "Pie in the Sky," the newer service, claims its uploading and downloading speeds are faster than the older service, "Cloudy but Steady Skies." You need to make a decision based on published access times for both services at different times and for varying file sizes. To make your decision, you purchase a statistical study, which indicates that average download time for Pie in the Sky is 0.77 sec. per MB and for Cloudy but Steady Skies is 0.84. Assume that n₁ = n₂ = 50, $\sigma$ ₁ = 0.2 and $\sigma$ ₂ = 0.3. With $\alpha$ =.05, the appropriate decision is ___.

A) reject the null hypothesis $\sigma$ ₁² < $\sigma$ ₂²
B) accept the alternate hypothesis $\mu$ ₁ - $\mu$ ₂ > 0
C) reject the alternate hypothesis n₁ = n₂ = 50
D) fail to reject the null hypothesis $\mu$ ₁ - $\mu$ ₂ = 0
E) do nothing

Question 60

Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies, is reviewing the order filling operations at her warehouses. Her goal is 100% of orders shipped within 24 hours. In previous years, neither warehouse has achieved the goal, but the East Coast Warehouse has consistently out-performed the West Coast Warehouse. Her staff randomly selected 200 orders from the West Coast Warehouse (population 1) and 400 orders from the East Coast Warehouse (population 2), and reports that 190 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 372 orders within 24 hours. Maureen's null hypothesis is ___.

A) π₁ - π₂ = 0
B) $\mu$ ₁ - $\mu$ ₂ = 0
C) p₁ - p₂ ≥ 0
D) $\mu$ ₁ - $\mu$ ₂ ≤ 0
E) $\mu$ ₁ - $\mu$ ₂ ≥ 0

Question 61

Maxwell Cantor, VP of human resources of Asimov Aerospace Industries Inc., is reviewing the technical certifications of employees in different divisions of the company. His goal is having 90% of technical employees with up-to-date certifications. The north-east division typically has maintained higher rates of up-to-date certifications than the southern division. He selects a random sample of 250 employees from the north-east division and 300 from the southern division and finds out that the number of employees with up-to-date certifications are 230 in the north-east division and 265 in the southern division. Maxwell's alternative hypothesis is ___.

A) $\mu$ ₁ - $\mu$ ₂ = 0
B) π₁ - π₂ ≥ 0
C) $\mu$ ₁ - $\mu$ ₂ ≤ 0
D) $\mu$ ₁ - $\mu$ ₂ ≥ 0
E) π₁ - π₂ = 0

Question 62

Suppose that the proportion of young adults who read at least one book per month is 0.15, and this proportion is the same in Boston and New York. Suppose that samples of size 400 are randomly drawn from each city. The standard deviation for the sampling distribution of differences between the first sample proportion and the second sample proportion (used to calculate the z score) is ___.

A) 0.0459
B) 0.0435
C) 0.0402
D) 0.0335
E) 0.0319

Question 63

Maxwell Cantor, VP of human resources of Asimov Aerospace Industries Inc., is reviewing the technical certifications of employees in different divisions of the company. His goal is having 90% of technical employees with up-to-date certifications. The north-east division typically has maintained higher rates of up-to-date certifications than the southern division. He selects a random sample of 250 employees from the north-east division and 300 from the southern division and finds out that the number of employees with up-to-date certifications are 230 in the north-east division and 265 in the southern division. Assuming $\alpha$ = 0.01, the critical z value is ___.

A) -2.33
B) 1.645
C) 1.96
D) 2.33
E) 2.576

Question 64

A researcher is interested in estimating the difference in two population proportions. A sample of 400 from each population results in sample proportions of.61 and.64. The point estimate of the difference in the population proportions is ___.

A) -0.030
B) 0.625
C) 0.000
D) 0.400
E) 0.500

Question 65

A product researcher wants to determine if there is a difference in the rate at which men and women become proficient at using a new software package. A study of 51 men and 46 women produced the following results:
At α = 0.05, is there evidence of a statistically significant difference between the time it takes men to become proficient at this particular software compared to the time it takes women? Assume equal population variances.

Question 66

Maxwell Cantor, VP of human resources of Asimov Aerospace Industries Inc., is reviewing the technical certifications of employees in different divisions of the company. His goal is having 90% of technical employees with up-to-date certifications. The north-east division typically has maintained higher rates of up-to-date certifications than the southern division. He selects a random sample of 250 employees from the north-east division and 300 from the southern division and finds out that the number of employees with up-to-date certifications are 230 in the north-east division and 265 in the southern division. Assuming $\alpha$ = 0.01, the observed z value is ___.

A) 1.027
B) 1.219
C) 1.427
D) 1.619
E) 1.827

Question 67

Are women more risk averse in the stock market? A sample of men and women were asked the following question: "If both the stock market and a stock you owned dropped 25% in three months, would you buy more shares while price is low?" Of 965 women, 338 said yes. Of 1066 men, 554 said yes.
At the α = 0.05 level of significance, is there evidence that the proportion of women who would buy more shares while the price is low is less than the proportion of men?

Question 68

A university administrator believes that business students are more likely to be working and going to school than their liberal arts majors. This information may lead to the business school offering courses in the evening hours while the liberal arts college maintains a daytime schedule. To test this theory the proportion of business students who are working at least 20 hours per week is compared to the proportion of liberal arts students who are working at least 20 hours per week. A random sample of 600 from the business school has been taken and it is determined that 480 students work at least 20 hours per week. A random sample of 700 liberal arts students showed that 350 work at least 20 hours per week. The observed z for this is ___.

A) 0.300
B) 0.624
C) 0.638
D) 11.22
E) 13.42

Question 69

Suppose that.06 of each of two populations possess a given characteristic. Samples of size 400 are randomly drawn from each population. What is the probability that the differences in sample proportions will be greater than 0.02?

A) 0.4535
B) 0.9535
C) 0.1170
D) 0.5465
E) 0.4650

Question 70

Maxwell Cantor, VP of human resources of Asimov Aerospace Industries Inc., is reviewing the technical certifications of employees in different divisions of the company. His goal is having 90% of technical employees with up-to-date certifications. The north-east division typically has maintained higher rates of up-to-date certifications than the southern division. He selects a random sample of 250 employees from the north-east division and 300 from the southern division and finds out that the number of employees with up-to-date certifications are 230 in the north-east division and 265 in the southern division. Maxwell's null hypothesis is ___.

A) $\mu$ ₁ - $\mu$ ₂ = 0
B) π₁ - π₂ ≥ 0
C) $\mu$ ₁ - $\mu$ ₂ ≤ 0
D) $\mu$ ₁ - $\mu$ ₂ ≥ 0
E) π₁ - π₂ = 0

Question 71

Maxwell Cantor, VP of human resources of Asimov Aerospace Industries Inc., is reviewing the technical certifications of employees in different divisions of the company. His goal is having 90% of technical employees with up-to-date certifications. The north-east division typically has maintained higher rates of up-to-date certifications than the southern division. He selects a random sample of 250 employees from the north-east division and 300 from the southern division and finds out that the number of employees with up-to-date certifications are 230 in the north-east division and 265 in the southern division. Assuming $\alpha$ = 0.01, the appropriate decision is ___.

A) do not reject the null hypothesis $\mu$ ₁ - $\mu$ ₂ = 0
B) do not reject the null hypothesis π₁ - π₂ = 0
C) reject the null hypothesis $\mu$ ₁ - $\mu$ ₂ = 0
D) reject the null hypothesis π₁ - π₂ = 0
E) do not reject the null hypothesis π₁ - π₂ ≥ 0

Question 72

A large corporation wants to determine whether or not the typing efficiency course given at a local college has any influence on typing speed of secretaries. A sample of 6 secretaries is selected, and they are sent to take the course. The typing speed of the secretaries in word per minute (WPM) are shown below:
At
, test if it can be concluded that taking the course increased the typing speed of the secretaries?