Math 240 Exam 2Name

TRUE/FALSE. Write ‘T’ if the statement is true and ‘F’ if the statement is false.

1) A 90 percent confidence interval will be wider than a 95 percent confidence interval,

ceteris paribus.

1)

2) The Central Limit Theorem says that, if n exceeds 30, the population will be normal.

2)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the

question.

3) The Central Limit Theorem (CLT) implies that:

A) the mean follows the same distribution as the population.

B) the population will be approximately normal if n ≥ 30.

C) the distribution of the mean is approximately normal for large n.

D) repeated samples must be taken to obtain normality.

3)

4) To estimate the average annual expenses of students on books and class materials, a

sample of size 36 is taken. The sample mean is $850 and the sample standard deviation

is $54. A 99 percent confidence interval for the population mean is:

A) $825.48 to $874.52

B) $826.82 to $873.18

C) $823.72 to $876.28

D) $832.36 to $867.64

4)

5) In constructing a 95 percent confidence interval, if you increase n to 4n, the width of

your confidence interval will be (assuming other things remain the same):

A) about 25 percent of its former width.

B) about four times wider.

C) about two times wider.

D) about 50 percent of its former width.

5)

6) Concerning confidence intervals, which statement is most nearly correct?

A) We use the Student’s t distribution when σ is unknown.

B) We should use z instead of t when n is large.

C) We use the Student’s t distribution to narrow the confidence interval.

6)

1

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the

question.

7) Read the news story below. Using the 95 percent confidence level, what sample 7)

size would be needed to estimate the true proportion of stores selling cigarettes to

minors with an error of ± 3 percent? Explain carefully, showing all steps in your

reasoning.

TRUE/FALSE. Write ‘T’ if the statement is true and ‘F’ if the statement is false.

8) The level of significance refers to the probability of making a Type II error.

8)

9) If we desire α = .10, then a p-value of .13 would lead us to reject the null hypothesis.

9)

10) For a given Ho and level of significance, if you reject the H0 for a one-tailed test, you

would also reject H0 for a two-tailed test.

10)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the

question.

11) Guidelines for the Jolly Blue Giant Health Insurance Company say that the average

hospitalization for a triple hernia operation should not exceed 30 hours. A diligent

auditor studied records of 16 randomly chosen triple hernia operations at Hackmore

Hospital and found a mean hospital stay of 40 hours with a standard deviation of 20

hours. “Aha!” she cried, “the average stay exceeds the guideline.” At α = .025, the

critical value for a right-tailed test of her hypothesis is:

A) 2.131

B) 1.960

C) 1.645

D) 1.753

2

11)

12) The level of significance is not:

A) a value between 0 and 1.

B) the chance of accepting a true null hypothesis.

C) the probability of a “false rejection.”

D) the likelihood of rejecting the null hypothesis when it is true.

12)

13) Dullco Manufacturing claims that its alkaline batteries last at least 40 hours on average

in a certain type of portable CD player. But tests on a random sample of 18 batteries

from a day’s large production run showed a mean battery life of 37.8 hours with a

standard deviation of 5.4 hours. To test DullCo’s hypothesis, the test statistic is:

A) -1.980

B) -1.960

C) -1.728

D) -2.101

13)

14) For a sample size of n = 100, and σ = 10, we want to test the hypothesis H0: µ = 100.

The sample mean is 103. The test statistic is:

A) 0.300

B) 3.000

C) 1.645

D) 1.960

14)

15) Which of the following is not a valid null hypothesis?

A) H0: µ ≠ 0

B) H0: µ = 0

C) H0: µ ≤ 0

15)

D) H0: µ ≥ 0

16) John wants to compare two means. His sample statistics were

and

equal variances, the pooled variance is:

A) 4.9

B) 3.8

16)

. Assuming

C) 5.1

D) 4.5

17) In a random sample of patient records in Cutter Memorial Hospital, six-month

postoperative exams were given in 90 out of 200 prostatectomy patients, while in

Paymor Hospital such exams were given in 110 out of 200 cases. In comparing these

two proportions, normality of the difference may be assumed because:

A) the samples are random, so the proportions are unbiased estimates.

B) nπ ≥ 10 and n(1 – π) ≥ 10 for each sample taken separately.

C) the probability of success can reasonably be assumed constant.

D) the populations are large enough to be assumed normal.

17)

18) Management of Melodic Kortholt Company compared absenteeism rates in two plants

on the third Monday in November. Of Plant A’s 800 employees, 120 were absent. Of

Plant B’s 1200 employees, 144 were absent. To compare the two proportions, the pooled

proportion is:

A) .140

B) .130

C) .132

D) .135

18)

3

19) Management of Melodic Kortholt Company compared absenteeism rates in two plants

on the third Monday in November. Of Plant A’s 800 employees, 120 were absent. Of

Plant B’s 1200 employees, 144 were absent. MegaStat’s results for a two-tailed test are

shown below.

The test statistic (shown as z = x.xx) is approximately:

A) 1.942

B) 1.645

C) 2.022

D) 1.960

20) A new policy of “flex hours” is proposed. Random sampling showed that 28 of 50

female workers favored the change, while 22 of 50 male workers favored the change.

Management wonders if there is a difference between the two groups. What is the test

statistic to test for a zero difference in the population proportions?

A) -1.255

B) 1.200

C) 1.321

D) 1.287

4

19)

20)

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