# MATHEMATICS

17) In a recent study of 42 eighth graders, the mean number of hours per week that they watched television was 19.6 with a standard deviation of 5.8 hours. Find the 98% confidence interval for the population mean. 17) _______

A) (17.5, 21.7) B) (14.1, 23.2) C) (18.3, 20.9) D) (19.1, 20.4)

18) In a sample of 10 randomly selected women, it was found that their mean height was 63.4 inches. From previous studies, it is assumed that the standard deviation, s, is 2.4. Construct the 95% confidence interval for the population mean. 18) _______

A) (61.9, 64.9) B) (58.1, 67.3) C) (59.7, 66.5) D) (60.8, 65.4)

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

19) There were 800 math instructors at a mathematics convention. Forty instructors were randomly selected and given an IQ test. The scores produced a mean of 130 with a standard deviation of 10. Find a 95% confidence interval for the mean of the 800 instructors. Use the finite population correction factor. 19) _____________

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

20) The standard IQ test has a mean of 97 and a standard deviation of 18. We want to be 95% certain that we are within 5 IQ points of the true mean. Determine the required sample size. 20) _______

A) 50 B) 8 C) 147 D) 1

21) A nurse at a local hospital is interested in estimating the birth weight of infants. How large a sample must she select if she desires to be 99% confident that the true mean is within 3 ounces of the sample mean? The standard deviation of the birth weights is known to be 8 ounces. 21) _______

A) 48 B) 47 C) 7 D) 6

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

22) In order to set rates, an insurance company is trying to estimate the number of sick days that full time workers at an auto repair shop take per year. A previous study indicated that the standard deviation was 2.2 days. a) How large a sample must be selected if the company wants to be 95% confident that the true mean differs from the sample mean by no more than 1 day? b) Repeat part (a) using a 98% confidence interval. Which level of confidence requires a larger sample size? Explain. 22) _____________

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

23) Find the critical value, _elementsubscript_element for c = 0.99 and n = 10. 23) _______

A) 3.250 B) 2.2821 C) 2.262 D) 1.833

24) Find the critical value, _elementsubscript_element, for c = 0.95 and n = 16. 24) _______

A) 2.131 B) 1.753 C) 2.602 D) 2.947

25) Find the critical value, _elementsubscript_element, for c = 0.90 and n = 15. 25) _______

A) 1.761 B) 1.345 C) 2.145 D) 2.624

26) Find the value of E, the maximum error of estimate, for c = 0. 90, n = 16 and s = 2.3. 26) _______

A) 1.01 B) 0.25 C) 0.77 D) 0.19

27) Find the value of E, the maximum error of estimate, for c = 0. 99, n = 10 and s = 3.8. 27) _______

A) 3.91 B) 3.39 C) 1.23 D) 3.81

28) Find the value of E, the maximum error of estimate, for c = 0. 99, n = 15 and s = 5.1. 28) _______

A) 3.92 B) 4.02 C) 3.46 D) 1.01

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

29) Construct a 98% confidence interval for the population mean, m. Assume the population has a normal distribution. A random sample of 20 college students has mean annual earnings of $3480 with a standard deviation of $668. 29) _____________

30) Construct a 95% confidence interval for the population mean, m. Assume the population has a normal distribution. In a random sample of 26 computers, the mean repair cost was $160 with a standard deviation of $34. 30) _____________

31) a) Construct a 95% confidence interval for the population mean, m. Assume the population has a normal distribution. In a random sample of 26 computers, the mean repair cost was $174 with a standard deviation of $37.

b) Suppose you did some research on repair costs for computers and found that the standard deviation is sigma = 37. Use the normal distribution to construct a 95% confidence interval for the population mean, m. Compare the results. 31) _____________