Deck 10: Fitness

Question 1

Sony would like to test the hypothesis that the average age of a PlayStation user is different from the average age of an Xbox user. A random sample of 36 PlayStation users had an average age of 34.2 years while a random sample of 30 Xbox users had an average age of 32.7 years. Assume that the population standard deviation for the age of PlayStation and Xbox users is 3.9 and 4.0 years, respectively. Sony would like to set ? = 0.10. If Population 1 is defined as PlayStation users and Population 2 is defined as Xbox users, the test statistic for this hypothesis test would be .

A)z $\bar { x }$ = 1.53
B)z $\bar { x }$ = 2.04
C)z $\bar { x }$ = - 1.27
D)z $\bar { x }$ = - 2.30

Answer 1

z $\bar { x }$ = 1.53

Question 2

The Centers for Disease Control (CDC)would like to test the hypothesis that the proportion of obese adults in the U.S. has increased this year when compared to last year. A random sample of 125 adults this year found that 56 were obese. Last year, a random sample of 140 adults found that 42 were obese. If Population 1 is defined as this year and Population 2 is defined as last year, and using α = 0.01, the conclusion for this hypothesis test would be that because the test statistic is

A)less than the critical value, the CDC cannot conclude that the proportion of obese adults in the
B)less than the critical value, the CDC can conclude that the proportion of obese adults in the
C)more than the critical value, the CDC can conclude that the proportion of obese adults in the U.S. has increased this year when compared to last year.
D)more than the critical value, the CDC cannot conclude that the proportion of obese adults in the U.S. has increased this year when compared to last year.

Answer 2

more than the critical value, the CDC can conclude that the proportion of obese adults in the U.S. has increased this year when compared to last year.

Question 3

The Centers for Disease Control (CDC)would like to test the hypothesis that the proportion of obese adults in the U.S. has increased this year when compared to last year. A random sample of 125 adults this year found that 56 were obese. Last year, a random sample of 140 adults found that 42 were obese. If Population 1 is defined as this year and Population 2 is defined as last year, the 98% confidence interval for the difference in population proportions is _______.

A)(0.011, 0.285)
B)(- 0.088, 0.384)
C)(0.089, 0.207)
D)(- 0.029, 0.325)

Answer 3

(0.011, 0.285)

Question 4

Sony would like to test the hypothesis that the average age of a PlayStation user is different from the average age of an Xbox user. A random sample of 36 PlayStation users had an average age of 34.2 years while a random sample of 30 Xbox users had an average age of 32.7 years. Assume that the population standard deviation for the age of PlayStation and Xbox users is 3.9 and 4.0 years, respectively. Sony would like to set α = 0.10. The 95% confidence interval for the difference in population means is ______.

A)(-1.70, 4.70)
B)(1.18, 1.82)
C)(0.65, 2.35)
D)(- 0.11, 3.11)

Question 5

Sony would like to test the hypothesis that the average age of a PlayStation user is different from the average age of an Xbox user. A random sample of 36 PlayStation users had an average age of 34.2 years while a random sample of 30 Xbox users had an average age of 32.7 years. Assume that the population standard deviation for the age of PlayStation and Xbox users is 3.9 and 4.0 years, respectively. Sony would like to set α = 0.10. The p- value for this hypothesis test would Be ______ .

A)0.1260
B)0.1722
C)0.0319
D)0.0643

Question 6

Progressive Insurance would like to test the hypothesis that a difference exists in the proportion of students in 12^th grade who text while driving when compared to the proportion of 11^th grade drivers who text. A random sample of 160 12^th grade students found that 84 texted while driving. A random sample of 175 11^th grade students found that 70 texted while driving. If Population 1 is defined as 12^th grade drivers and Population 2 is defined as 11th grade drivers, and using α = 0.05, which one of the following statements is true?

A)Because the p- value is less than α, Progressive Insurance can conclude that a difference exists in the proportion of students in 12^th grade who text while driving when compared to the proportion of 11^th grade drivers who text.
B)Because the p- value is greater than α, Progressive Insurance can conclude that a difference exists in the proportion of students in 12^th grade who text while driving when compared to the proportion of 11^th grade drivers who text.
C)Because the p- value is greater than α, Progressive Insurance cannot conclude that a difference exists in the proportion of students in 12th grade who text while driving when compared to the proportion of 11^th grade drivers who text.
D)Because the p- value is less than α, Progressive Insurance cannot conclude that a difference exists in the proportion of students in 12^th grade who text while driving when compared to the proportion of 11^th grade drivers who text.

Question 7

The Centers for Disease Control (CDC)would like to test the hypothesis that the proportion of obese adults in the U.S. has increased this year when compared to last year. A random sample of 125 adults this year found that 56 were obese. Last year, a random sample of 140 adults found that 42 were obese. If Population 1 is defined as this year and Population 2 is defined as last year, the test statistic for this hypothesis test would be ______ .

A)z_p = - 2.20
B)z_p = 0.95
C)z_p = 2.49
D)z_p = - 1.52

Question 8

AT&T would like to test the hypothesis that the proportion of 18- to 34- year- old Americans that own a cell phone is less than the proportion of 35- to 49- year- old Americans. A random sample of 200 18- to 34- year- old Americans found that 126 owned a smartphone. A random sample of 175 35- to 49- year- old Americans found that 119 owned a smartphone. If Population 1 is defined as 18- to 34- year- old Americans and Population 2 is defined as 35- to 49- year- old Americans, which one of the following statements is true?

A)Because the 98% confidence interval includes zero, AT&T can conclude that the proportion of 18- to 34- year- old Americans that own a cell phone is less than the proportion of 35- to
B)Because the 98% confidence interval does not include zero, AT&T cannot conclude that the proportion of 18- to 34- year- old Americans that own a cell phone is less than the proportion of 35- to 49- year- old Americans.
C)Because the 98% confidence interval includes zero, AT&T cannot conclude that the proportion of 18- to 34- year- old Americans that own a cell phone is less than the proportion of 35- to 49- year- old Americans.
D)Because the 98% confidence interval does not include zero, AT&T can conclude that the proportion of 18- to 34- year- old Americans that own a cell phone is less than the proportion of 35- to 49- year- old Americans.

Question 9

Sony would like to test the hypothesis that the average age of a PlayStation user is different from the average age of an Xbox user. A random sample of 36 PlayStation users had an average age of 34.2 years while a random sample of 30 Xbox users had an average age of 32.7 years. Assume that the population standard deviation for the age of PlayStation and Xbox users is 3.9 and 4.0 years, respectively. Sony would like to set α = 0.10. Which one of the following statements is true?

A)Because the 90% confidence interval does not include zero, we fail to reject the null hypothesis and can conclude that the average age of PlayStation users is different from the average age of Xbox users.
B)Because the 90% confidence interval does not include zero, we reject the null hypothesis and can conclude that the average age of PlayStation users is different from the average age of Xbox users.
C)Because the 90% confidence interval includes zero, we fail to reject the null hypothesis and cannot conclude that the average age of PlayStation users is different from the average age of Xbox users.
D)Because the 90% confidence interval includes zero, we fail to reject the null hypothesis and conclude that the average age of PlayStation users is equal to the average age of Xbox users.

Question 10

The Centers for Disease Control (CDC)would like to test the hypothesis that the proportion of obese adults in the U.S. has increased this year when compared to last year. A random sample of 125 adults this year found that 56 were obese. Last year, a random sample of 140 adults found that 42 were obese. If Population 1 is defined as this year and Population 2 is defined as last year, and using α = 0.01, which one of the following statements is true?

A)Because the p- value is greater than α, the CDC cannot conclude that the proportion of obese adults in the U.S. has increased this year when compared to last year.
B)Because the p- value is greater than α, the CDC can conclude that the proportion of obese adults in the U.S. has increased this year when compared to last year.
C)Because the p- value is less than α, the CDC can conclude that the proportion of obese adults in the U.S. has increased this year when compared to last year.
D)Because the p- value is less than α, the CDC cannot conclude that the proportion of obese adults in the U.S. has increased this year when compared to last year.

Question 11

AT&T would like to test the hypothesis that the proportion of 18- to 34- year- old Americans that own a cell phone is less than the proportion of 35- to 49- year- old Americans. A random sample of 200 18- to 34- year- old Americans found that 126 owned a smartphone. A random sample of 175 35- to 49- year- old Americans found that 119 owned a smartphone. If Population 1 is defined as 18- to 34- year- old Americans and Population 2 is defined as 35- to 49- year- old Americans, the p- value for this hypothesis test is _______.

A)0.1562
B)0.0026
C)0.0087
D)0.1025

Question 12

The Centers for Disease Control (CDC)would like to test the hypothesis that the proportion of obese adults in the U.S. has increased this year when compared to last year. A random sample of 125 adults this year found that 56 were obese. Last year, a random sample of 140 adults found that 42 were obese. If Population 1 is defined as this year and Population 2 is defined as last year, the p- value for this hypothesis test is _.

A)0.1511
B)0.1877
C)0.0064
D)0.0301

Question 13

Progressive Insurance would like to test the hypothesis that a difference exists in the proportion of students in 12^th grade who text while driving when compared to the proportion of 11th grade drivers who text. A random sample of 160 12^th grade students found that 84 texted while driving. A random sample of 175 11^th grade students found that 70 texted while driving. If Population 1 is defined as 12^th grade drivers and Population 2 is defined as 11^th grade drivers, the 95% confidence interval for the difference in population proportions is ______.

A)(- 0.119, 0.369)
B)(0.018, 0.231)
C)(- 0.037, 0.287)
D)(0.103, 0.147)

Question 14

Sony would like to test the hypothesis that the average age of a PlayStation user is different from the average age of an Xbox user. A random sample of 36 PlayStation users had an average age of 34.2 years while a random sample of 30 Xbox users had an average age of 32.7 years. Assume that the population standard deviation for the age of PlayStation and Xbox users is 3.9 and 4.0 years, respectively. Sony would like to set α = 0.10. The conclusion for this hypothesis test would be that because the absolute value of the test statistic is

A)more than the absolute value of the critical value, we can conclude that the average age of PlayStation users is equal to the average age of Xbox users.
B)more than the absolute value of the critical value, we can conclude that the average age of PlayStation users is different from the average age of Xbox users.
C)less than the absolute value of the critical value, we cannot conclude that the average age of PlayStation users is equal to the average age of Xbox users.
D)less than the absolute value of the critical value, we cannot conclude that the average age of PlayStation users is different from the average age of Xbox users.

Question 15

The Centers for Disease Control (CDC)would like to test the hypothesis that the proportion of obese adults in the U.S. has increased this year when compared to last year. A random sample of 125 adults this year found that 56 were obese. Last year, a random sample of 140 adults found that 42 were obese. If Population 1 is defined as this year and Population 2 is defined as last year, the correct hypothesis statement for this hypothesis test would be

A)H₀: p1 - p2 c 0; H₁: p1 - p2 < 0.
B)H₀: p1 - p2 = 0; H₁: p1 - p2 × 0.
C)H₀: p1 - p2 < 0; H₁: p1 - p2 c 0.
D)H₀: p1 - p2 c 0; H₁: p1 - p2 > 0.

Question 16

AT&T would like to test the hypothesis that the proportion of 18- to 34- year- old Americans that own a cell phone is less than the proportion of 35- to 49- year- old Americans. A random sample of 200 18- to 34- year- old Americans found that 126 owned a smartphone. A random sample of 175 35- to 49- year- old Americans found that 119 owned a smartphone. If Population 1 is defined as 18- to 34- year- old Americans and Population 2 is defined as 35- to 49- year- old Americans, the correct hypothesis statement for this hypothesis test would be ______

A)H₀: p1 - p2 c 0; H₁: p1 - p2 > 0
B)H₀: p1 - p2 c 0; H₁: p1 - p2 < 0
C)H₀: p1 - p2 = 0; H₁: p1 - p2 × 0
D)H₀: p1 - p2 < 0; H₁: p1 - p2 c 0

Question 17

The Centers for Disease Control (CDC)would like to test the hypothesis that the proportion of obese adults in the U.S. has increased this year when compared to last year. A random sample of 125 adults this year found that 56 were obese. Last year, a random sample of 140 adults found that 42 were obese. If Population 1 is defined as this year and Population 2 is defined as last year, which one of the following statements is true?

A)Because the 98% confidence interval includes zero, the CDC cannot conclude that the proportion of obese adults in the U.S. has increased this year when compared to last year.
B)Because the 98% confidence interval does not include zero, the CDC cannot conclude that the proportion of obese adults in the U.S. has increased this year when compared to last year.
C)Because the 98% confidence interval does not include zero, the CDC can conclude that the proportion of obese adults in the U.S. has increased this year when compared to last year.
D)Because the 98% confidence interval includes zero, the CDC can conclude that the proportion of obese adults in the U.S. has increased this year when compared to last year.

Question 18

Progressive Insurance would like to test the hypothesis that a difference exists in the proportion of students in 12^th grade who text while driving when compared to the proportion of 11^th grade drivers who text. A random sample of 160 12^th grade students found that 84 texted while driving. A random sample of 175 11th grade students found that 70 texted while driving. If Population 1 is defined as 12^th grade drivers and Population 2 is defined as 11th grade drivers, and using α = 0.05, the conclusion for this hypothesis test would be that because the absolute value of the test statistic is

A)less than the absolute value of the critical value, Progressive Insurance cannot conclude that a difference exists in the proportion of students in 12th grade who text while driving when compared to the proportion of 11th grade drivers who text.
B)more than the absolute value of the critical value, Progressive Insurance cannot conclude that a difference exists in the proportion of students in 12th grade who text while driving when compared to the proportion of 11th grade drivers who text.
C)more than the absolute value of the critical value, Progressive Insurance can conclude that a difference exists in the proportion of students in 12th grade who text while driving when compared to the proportion of 11th grade drivers who text.
D)less than the absolute value of the critical value, Progressive Insurance can conclude that a difference exists in the proportion of students in 12^th grade who text while driving when compared to the proportion of 11^th grade drivers who text.

Question 19

Progressive Insurance would like to test the hypothesis that a difference exists in the proportion of students in 12th grade who text while driving when compared to the proportion of 11th grade drivers who text. A random sample of 160 12th grade students found that 84 texted while driving. A random sample of 175 11th grade students found that 70 texted while driving. If Population 1 is defined as 12th grade drivers and Population 2 is defined as 11th grade drivers, and using α = 0.05, the critical value for this hypothesis test would be .

A)2.33
B)1.645
C)1.96
D)2.05

Question 20

Two real estate companies, Century 21 and RE/MAX, compete with one another in a local market. The manager of the Century 21 office would like to advertise that homes listed with RE/MAX average more than 10 days on the market when compared to homes listed with his company. The following data shows the sample size and average number of days on the market for the two companies along with the population standard deviations.

A)Because the 80% confidence interval does not include 10, the manager at Century 21 can reject the null hypothesis and claim that homes listed with RE/MAX average more than 10 days on the market when compared to homes listed with his company.
B)Because the 80% confidence interval does not include zero, the manager at Century 21 can reject the null hypothesis and cannot claim that homes listed with RE/MAX average more than 10 days on the market when compared to homes listed with his company.
C)Because the 80% confidence interval includes 10, the manager at Century 21 can fail to reject the null hypothesis and claim that homes listed with RE/MAX average more than 10 days on the market when compared to homes listed with his company.
D)Because the 80% confidence interval includes zero, the manager at Century 21 can fail to reject the null hypothesis and claim that homes listed with RE/MAX average more than 10 days on the market when compared to homes listed with his company.

Question 21

When in doubt about your assumption that the population variances are equal when comparing two population means, the best strategy is to proceed with the unequal variances test.

Question 22

When conducting a hypothesis test comparing two populations with dependent samples, the sample sizes must be equal.

Question 23

The pooled variance is used to calculate the test statistics for comparing two population means when the population variances are assumed to be unequal.

Question 24

A hypothesis test using dependent samples is known as a matched- pair test.

Question 25

When the confidence interval for the difference between two means does not include zero when testing H0: µ1 - µ2 = 0, we have support that a significant difference between population means does exist.

Question 26

When calculating the degrees of freedom for a hypothesis test comparing two population means with population variances that are unknown and assumed to be unequal, always round up the degrees of freedom to the next highest integer. This makes it more challenging to reject the null hypothesis which is a more conservative approach.

Question 27

The sampling distribution for the difference in means is the result of subtracting the sampling distribution for the mean of one sample from the sampling distribution for the mean of a second sample.

Question 28

If we are sampling from a normal distribution to conduct a hypothesis test, then our sampling distribution will only be normally distributed if our sample size is 30 or more.

Question 29

The approximate standard error of the difference between population proportions uses the sample proportions to estimate the values of the population proportions when determining the standard deviation.

Question 30

The standard error of the difference between two means describes the variation in the difference between two sample means.

Question 31

When conducting a hypothesis test comparing two populations with independent samples, the sample sizes must be equal.

Question 32

The sampling distribution for the difference in proportions is the result of subtracting one sampling distribution for the proportion from a second sampling distribution for the proportion.

Question 33

Two samples are independent of one another when the results you observe when sampling from one population have no impact on the results you observe when sampling from the second population.

Question 34

When performing a hypothesis test comparing two population means, we need to assign Population 1 to the larger sample mean and Population 2 to the smaller sample mean.

Question 35

The hypothesis statement H0: µ1 - µ2 = 0 is an example of a two- tail hypothesis test.

Question 36

When conducting a hypothesis test comparing two populations with independent samples, each observation from one sample is related to an observation from the other sample.

Question 37

The degrees of freedom for the appropriate critical value with a hypothesis test comparing two population means with population variances that are unknown but assumed to be equal are determined by n1 + n2 - 1.

Question 38

The pooled variance is the weighted average of two sample variances drawn from two populations.

Question 39

The standard error of the difference between population proportions describes the result of subtracting one sample proportion from a second sample proportion.

Question 40

The test statistic for hypothesis tests comparing two population proportions follows the Student's
t- distribution.