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```					Name:_________Key______________________                                          STA 291 Sec. 016-021 Lab #7

Practice Exam Questions

1. A child psychologist wants to estimate the percentage of fathers who watch their preschool-aged children while the
mother works. What sample size should be obtained if she wants the estimate to be within 3 percentage points with
95% confidence if:

(a) she uses a 1995 estimate obtained from the U.S. Census Bureau of 18.5%?

(b) she doesn’t use any prior estimates?

2. Sample weights of newborn babies born in two adjacent counties yielded the following data:          ,        ,
,       ,         , and        . If we want to conduct a hypothesis test to determine if we have evidence
that the mean weights of newborn babies are different for the two counties, what hypotheses should we use?

___              ___                     ___               ___

3. According to the National Youth Survey, 48% of 835 male youths surveyed were raised in a single-parent family.
Suppose we want to determine if there is evidence that more than 45% of male youths are raised in a single parent
family. In this case, the p-value is the probability that ________, under the assumption that ________. Written as an
Excel function call, the p-value is: ________.

First Blank:___        _________                  Second Blank:____         _________

Third Blank:__                                            ____OR____                                            __

4. A statistician wants to test            against           . The statistician reported that      ,       , and
. What is the p-value of the test, as computed using Excel?
(a)
(b)
(c)
(d)

5. A publishing company wants to test whether secretaries type faster using word processor brand 1 or brand 2. Twelve
secretaries are tested on each word processor, and their speeds in words per minute are recorded. Using and , a
95% confidence interval is calculated:                . If we were to test            against            using
significance level        , what would the appropriate conclusion be?
(a)   Reject the null hypothesis.
(b)   Fail to reject the null hypothesis.
(c)   Reject the alternative hypothesis.
(d)   Fail to reject the alternative hypothesis.

6. The Wilson Company is doing tests to determine whether yellow, white, or orange tennis balls are easiest to see.
During testing, it became necessary to estimate what proportion of the male population is color-blind, because color-
blind males have difficulty seeing the orange ball. In a random sample of 1600 males, 240 were color-blind.

(a) Construct and interpret a 99% confidence interval for p, the proportion of the male population that is color-blind.
Note: The critical value is 2.576.

“We are 99% confident that the interval (.127, .173) contains p, the proportion of the male population that is color-
blind.”

(b) How would you obtain the critical value given in part (a) using an Excel function?

7. At a university, last year’s freshman class had a mean ACT score of 21.5. A sample of 200 students in this year’s
freshman class had a sample mean score of 21.3, with a sample standard deviation of 5.8. Using a .05 level of
significance, is there evidence that this year’s freshman class has a different mean ACT score than last year’s freshman
class? Perform the appropriate hypothesis test.

(a) State the appropriate hypotheses.

vs.

(b) What is the standard error of the sampling distribution of the sample mean?

(c) What is the test statistic?

(d) Assuming that the assumptions and conditions for inference are met, determine the p-value or the critical value for
the rejection region. In either case, write your answer using an Excel function.

OR

(e) Using your answer to part (d) (and possibly part (c)), explain how you would determine if you have enough evidence
to reject the null hypothesis.

P-value: Reject H0 if:
Critical Value/Rejection Region: Reject H0 if:

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