Deck 10: Inference About Means and Proportions With Two Populations

Question 1

Independent random samples of managers' yearly salaries (in $1000s) randomly selected from governmental and private organizations provided the following information. At 95% confidence, test to determine if there is a significant difference between the average salaries of the managers in the two sectors. ​

Answer 1

​
H₀: μ_{1 -} μ₂ = 0
H_a: μ_{1 -} μ₂ ≠ 0
df = 56; test statistic t = 2.021; p-value (two-tailed) is between .02 and .05; reject H₀
​

Question 2

If two independent large samples are selected from two populations, the sampling distribution of the difference between the two sample means _____.

A) can be approximated by a Poisson distribution
B) will have a variance of 1
C) can be approximated by a normal distribution
D) will have a mean of 1

Answer 2

can be approximated by a normal distribution

Question 3

A company wants to identify which of two production methods has the smaller completion time. One sample of workers is randomly selected and each worker first uses one method and then uses the other method. The sampling procedure being used to collect completion time data is based on _____ samples.

A) cross
B) pooled
C) independent
D) matched

Answer 3

matched

Question 4

In testing the null hypothesis H₀: μ1 - μ2 = 0, the computed test statistic is z = -1.66. The corresponding p-value is _____.

A) .0485
B) .0970
C) .9515
D) .9030

Question 5

If the alternative hypothesis is that proportion of items in population 1 is larger than the proportion of items in population 2, then the null hypothesis should be _____.

A) p₁ - p₂ < 0
B) p1 - p₂ = 0
C) p1 - p₂ > 0
D) p1 - p₂ ≤ 0

Question 6

A comparative study of organic and conventionally grown produce was checked for the presence of E. coli. Results are summarized below. Is there a significant difference in the proportion of E. coli in organic versus conventionally grown produce? Test at α = .10.

Question 7

The following shows the monthly sales in units of six salespersons before and after a bonus plan was introduced. At 95% confidence, determine whether the bonus plan has increased sales significantly. (For the following matched samples, let d = After - Before.)

Question 8

To compute an interval estimate for the difference between the means of two populations, the t distribution _____.

A) is restricted to small sample situations
B) is not restricted to small sample situations
C) can be applied when the populations have equal means
D) None of the answers is correct.

Question 9

Independent simple random samples are selected to test the difference between the means of two populations whose standard deviations are not known. We are unwilling to assume that the population variances are equal. The sample sizes are n₁ = 25 and n₂ = 35. The correct distribution to use is the t distribution with ______ degrees of freedom.

A) 25
B) 35
C) 58
D) The correct degrees of freedom cannot be calculated without being given the sample standard deviations.

Question 10

The sampling distribution of $\bar { p } _ { 1 } - \bar { p } _ { 2 }$ is approximated by a _____.

A) normal distribution
B) t distribution with n₁ + n₂ degrees of freedom
C) t distribution with n₁ + n₂ - 1 degrees of freedom
D) t distribution with n₁ + n₂ + 2 degrees of freedom

Question 11

When developing an interval estimate for the difference between two sample means, with sample sizes of n₁ and n₂, _____.

A) n₁ must be equal to n₂
B) n₁ must be smaller than n₂
C) n₁ must be larger than n₂
D) n₁ and n₂ can be of different sizes

Question 12

The office of records at a university has stated that the proportion of incoming female students who major in business has increased. A random sample of female students selected several years ago is compared with a random sample of female students selected this year. Results are summarized below. Has the proportion increased significantly? Test at α = .10.

Question 13

To construct an interval estimate for the difference between the means of two populations when the standard deviations of the two populations are unknown, we must use a t distribution with (let n₁ be the size of sample 1 and n₂ the size of sample 2) _____ degrees of freedom.

A) n₁ + n₂
B) n₁ + n₂ - 1
C) n₁ + n₂ - 2
D) n₁ - n₂ + 2

Question 14

In a sample of 100 Republicans, 60 favored the president's anti-drug program. While in a sample of 150 Democrats, 84 favored his program. At 95% confidence, test to see if there is a significant difference in the proportions of the Democrats and the Republicans who favored the president's anti-drug program.

Question 15

The following data give the number of computer units sold per day by a random sample of six salespersons before and after a bonus plan was implemented. At 95% confidence, test to see if the bonus plan was effective. That is, did the bonus plan actually increase sales?

Question 16

The following information was obtained from matched samples regarding the productivity of four individuals using two different methods of production. Let d = Method 1 - Method 2. Is there a significant difference between the productivity of the two methods? Let α = .05.

Question 17

The standard error of $\bar { x } _ { 1 } - \bar { x } _ { 2 }$ is the _____.

A) variance of $\bar { x } _ { 1 } - \bar { x } _ { 2 }$
B) variance of the sampling distribution of $\bar { x } _ { 1 } - \bar { x } _ { 2 }$
C) standard deviation of the sampling distribution of $\bar { x } _ { 1 } - \bar { x } _ { 2 }$
D) difference between the two means

Question 18

Independent simple random samples are selected to test the difference between the means of two populations whose variances are not known. The sample sizes are n₁ = 32 and n₂ = 40. The correct distribution to use is the _____ distribution.

A) binomial
B) t
C) normal
D) uniform

Question 19

A poll was administered this year asking college students if they considered themselves overweight. A similar poll was administered five years ago. Results are summarized below. Has the proportion increased significantly? Let α = 0.05.

Question 20

When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as _____.

A) corresponding samples
B) matched samples
C) independent samples
D) None of the answers is correct.

Question 21

A survey was recently conducted to determine if consumers spend more on computer-related purchases via the Internet or store visits. Assume a random sample of eight respondents provided the following data on their computer-related purchases during a 30-day period. Using a .05 level of significance, can we conclude that consumers spend more on computer-related purchases by way of the Internet than by visiting stores?
​
​ ​
​