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Math 104 Midterm | Complete Solution
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1. A 99% confidence interval estimate can be interpreted to mean that

a. if all possible samples are taken and confidence interval estimates are developed, 99% of them would include the true population mean somewhere within their interval.
b. we have 99% confidence that we have selected a sample whose interval does include the population mean.
c. Both of the above.
d. None of the above.

2. Which of the following is not true about the Student's t distribution?
a. It has more area in the tails and less in the center than does the normal distribution.
b. It is used to construct confidence intervals for the population mean when the population standard deviation is known.
c. It is bell shaped and symmetrical.
d. As the number of degrees of freedom increases, the t distribution approaches the normal distribution.

3. A confidence interval was used to estimate the proportion of statistics students that are females. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Based
on the interval above, is the population proportion of females equal to 0.60?
a. No, and we are 90% sure of it.
b. No. The proportion is 54.17%.
c. Maybe. 0.60 is a believable value of the population proportion based on the information above.
d. Yes, and we are 90% sure of it.

4. A confidence interval was used to estimate the proportion of statistics students that are female. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Using
the information above, what size sample would be necessary if we wanted to estimate the true proportion to within 0.08 using 95% confidence?
a. 105
b. 150
c. 420
d. 597

5. When determining the sample size necessary for estimating the true population mean, which factor is not considered when sampling with replacement?
a. The population size.
b. The population standard deviation.
c. The level of confidence desired in the estimate.
d. The allowable or tolerable sampling error.

6. An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be \$1,000. A random sample of 50 individuals resulted in an average income
of \$15,000. What is the upper end point in a 99% confidence interval for the average income?
a. \$15,052
b. \$15,141
c. \$15,330
d. \$15,364

7. An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be \$1,000. A random sample of 50 individuals resulted in an average income
of \$15,000. What sample size would the economist need to use for a 95% confidence interval if the width of the interval should not be more than
\$100?
a. n = 1537
b. n = 385
c. n = 40
d. n = 20

8. The head librarian at the Library of Congress has asked her assistant for an interval estimate of the mean number of books checked out each day. The assistant provides the following interval estimate: from 740 to 920 books per day. If the head librarian knows that the population standard deviation is 150 books checked out per day, and she asked her assistant to use 25 days of data to construct the interval estimate, what confidence level can she attach to the interval estimate?
a. 99.7%
b. 99.0%
c. 98.0%
d. 95.4%

9. Which of the following would be an appropriate null hypothesis?
a. The population proportion is less than 0.65.
b. The sample proportion is less than 0.65.
c. The population proportion is no less than 0.65.
d. The sample proportion is no less than 0.65.

10. If we are performing a two-tailed test of whether = 100, the probability of detecting a shift of the mean to 105 will be ________ the probability of detecting a shift of the mean to 110.
a. less than
b. greater than
c. equal to
d. not comparable to

11. Which of the following statements is not true about the level of significance in a hypothesis test?

a. The larger the level of significance, the more likely you are to reject the null hypothesis.
b. The level of significance is the maximum risk we are willing to accept in making a Type I error.
c. The significance level is also called the level.
d. The significance level is another name for Type II error.

12. A _________________ is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis.
a. significance level
b. critical value
c. test statistic
d. parameter

TABLE 7-2
A student claims that he can correctly identify whether a person is a business major or an agriculture major by the way the person dresses. Suppose in actuality that he can correctly identify a business major 87% of
the time, while 16% of the time he mistakenly identifies an agriculture major as a business major. Presented with one person and asked to identify the major of this person (who is either a business or agriculture major), he
considers this to be a hypothesis test with the null hypothesis being that the person is a business major and the alternative that the person is an agriculture major.

13. Referring to Table 7-2, what would be a Type I error?
a. Saying that the person is a business major when in fact the person is a business major.
b. Saying that the person is a business major when in fact the person is an agriculture major.
c. Saying that the person is an agriculture major when in fact the person is a business major.
d. Saying that the person is an agriculture major when in fact the person is an agriculture major.

TABLE 7-6
The quality control engineer for a furniture manufacturer is interested in the mean amount of force necessary to produce cracks in stressed oak furniture. The mean for unstressed furniture is 650 psi. She performs a two-tailed test of the null hypothesis that the mean for the stressed oak furniture is 650. The calculated value of the Z test statistic is a positive number that leads to a p value of 0.080 for the test.

14. Referring to Table 7-6, suppose the engineer had decided that the alternative hypothesis to test was that the mean was less than 650. What would be the p value of this one-tailed test?
a. 0.040
b. 0.160
c. 0.840
d. 0.960

15. The t test for the mean difference between 2 related populations assumes that the respective
a. sample sizes are equal.
b. sample variances are equal.
c. populations are approximately normal or sample sizes are large enough.
d. All of the above.

16. In testing for differences between the means of 2 related populations
the null hypothesis is:
a. H0: D = 2.
b. H0: D = 0.
c. H0: D < 0.
d. H0: D > 0.

17. To use the Wilcoxon Rank Sum Test as a test for location, we must assume that
a. the obtained data are either ranks or numerical measurements both within and between the 2 samples.
b. both samples are randomly and independently drawn from their respective populations.
c. both underlying populations from which the samples were drawn are equivalent in shape and dispersion.
d. All the above.

TABLE 8-4
A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. A random sample of 100 families from Gotham and
a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.
Gotham: G = 35 months, sG2 = 900 Metropolis: M = 50 months, sM2 = 1050
18. Referring to Table 8-4, what is(are) the critical value(s) of the
relevant hypothesis test if the level of significance is 0.01?
a. t  Z = -1.96
b. t  Z = 1.96
c. t  Z = -2.080
d. t  Z = -2.33

19. Referring to Table 8-4, what is the standardized value of the estimate of the mean of the sampling distribution of the difference between sample means?
a. -8.75
b. -3.75
c. -2.33
d. -1.96

TABLE 8-5
To test the effects of a business school preparation course, eight (8) students took a general business test before and after the course. The results are given below.
Exam Score Exam Score
Student Before Course (1) After Course (2)
1 530 670
2 690 770
3 910 1000
4 700 710
5 450 550
6 820 870
7 820 770
8 630 610

20. Referring to Table 8-5, at the 0.05 level of significance, the decision for this hypothesis test would be: a. reject the null hypothesis.
b. do not reject the null hypothesis.
c. reject the alternative hypothesis.
d. It cannot be determined from the information given.

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