# MATHEMATICS

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

10) A random sample of 150 students has a grade point average with a mean of 2.86 and with a standard deviation of 0.78. Construct the confidence interval for the population mean, m, if c = 0.98. 10) _______

A) (2.71, 3.01) B) (2.51, 3.53) C) (2.43, 3.79) D) (2.31, 3.88)

11) A random sample of 40 students has a test score with overbar(x) = 81.5 and s = 10.2. Construct the confidence interval for the population mean, m if c = 0.90. 11) _______

A) (78.8, 84.2) B) (51.8, 92.3) C) (66.3, 89.1) D) (71.8, 93.5)

12) A random sample of 40 students has a mean annual earnings of $3120 and a standard deviation of $677. Construct the confidence interval for the population mean, m if c = 0.95. 12) _______

A) ($2910, $3330) B) ($210, $110)

C) ($4812, $5342) D) ($1987, $2346)

13) A random sample of 56 fluorescent light bulbs has a mean life of 645 hours with a standard deviation of 31 hours. Construct a 95% confidence interval for the population mean. 13) _______

A) (636.9, 653.1) B) (539.6, 551.2)

C) (112.0, 118.9) D) (712.0, 768.0)

14) A group of 49 randomly selected students has a mean age of 22.4 years with a standard deviation of 3.8. Construct a 98% confidence interval for the population mean. 14) _______

A) (21.1, 23.7) B) (20.3, 24.5) C) (19.8, 25.1) D) (18.8, 26.3)

15) A group of 40 bowlers showed that their average score was 192 with a standard deviation of 8. Find the 95% confidence interval of the mean score of all bowlers. 15) _______

A) (189.5, 194.5) B) (186.5, 197.5)

C) (188.5, 195.6) D) (187.3, 196.1)

16) In a random sample of 60 computers, the mean repair cost was $150 with a standard deviation of $36. Construct a 99% confidence interval for the population mean. 16) _______

A) ($138, $162) B) ($18, $54) C) ($238, $274) D) ($537, $654)

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) _____________

32) A manufacturer receives an order for fluorescent light bulbs. The order requires that the bulbs have a mean life span of 850 hours. The manufacturer selects a random sample of 25 fluorescent light bulbs and finds that they have a mean life span of 845 hours with a standard deviation of 15 hours. Test to see if the manufacturer is making acceptable light bulbs. Use a 95% confidence level. Assume the data are normally distributed. 32) _____________

33) Construct a 95% confidence interval for the population mean, m. Assume the population has a normal distribution. A sample of 20 college students had mean annual earnings of $3120 with a standard deviation of $677. 33) _______

A) ($2803, $3437) B) ($1324, $1567)

C) ($2135, $2567) D) ($2657, $2891)

34) Construct a 90% confidence interval for the population mean, m. Assume the population has a normal distribution. A sample of 15 randomly selected students has a grade point average of 2.86 with a standard deviation of 0.78. 34) _______

A) (2.51, 3.21) B) (2.41, 3.42) C) (2.37, 3.56) D) (2.28, 3.66)

35) Construct a 95% confidence interval for the population mean, m. Assume the population has a normal distribution. A sample of 25 randomly selected students has a mean test score of 81.5 with a standard deviation of 10.2. 35) _______

A) (77.29, 85.71) B) (56.12, 78.34)

C) (66.35, 69.89) D) (87.12, 98.32)

36) Construct a 95% confidence interval for the population mean, m. Assume the population has a normal distribution. A random sample of 16 fluorescent light bulbs has a mean life of 645 hours with a standard deviation of 31 hours. 36) _______

A) (628.5, 661.5) B) (876.2, 981.5)

C) (531.2, 612.9) D) (321.7, 365.8)

37) Construct a 99% confidence interval for the population mean, m. Assume the population has a normal distribution. A group of 19 randomly selected students has a mean age of 22.4 years with a standard deviation of 3.8 years. 37) _______

A) (19.9, 24.9) B) (16.3, 26.9) C) (17.2, 23.6) D) (18.7, 24.1)

38) Construct a 98% confidence interval for the population mean, m. Assume the population has a normal distribution. A study of 14 bowlers showed that their average score was 192 with a standard deviation of 8. 38) _______

A) (186.3, 197.7) B) (222.3, 256.1)

C) (328.3, 386.9) D) (115.4, 158.8)

39) Construct a 90% confidence interval for the population mean, m. Assume the population has a normal distribution. In a recent study of 22 eighth graders, the mean number of hours per week that they watched television was 19.6 with a standard deviation of 5.8 hours. 39) _______

A) (17.47, 21.73) B) (18.63, 20.89)

C) (5.87, 7.98) D) (19.62, 23.12)

40) A random sample of 10 parking meters in a beach community showed the following incomes for a day. Assume the incomes are normally distributed.

$3.60 $4.50 $2.80 $6.30 $2.60 $5.20 $6.75 $4.25 $8.00 $3.00

Find the 95% confidence interval for the true mean. 40) _______

A) ($3.39, $6.01) B) ($2.11, $5.34)

C) ($4.81, $6.31) D) ($1.35, $2.85)

41) The grade point averages for 10 randomly selected high school students are listed below. Assume the grade point averages are normally distributed.

2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8

Find a 98% confidence interval for the true mean. 41) _______

A) (1.55, 3.53) B) (0.67, 1.81) C) (2.12, 3.14) D) (3.11, 4.35)

42) A local bank needs information concerning the checking account balances of its customers. A random sample of 15 accounts was checked. The mean balance was $686.75 with a standard deviation of $256.20. Find a 98% confidence interval for the true mean. Assume that the account balances are normally distributed. 42) _______

A) ($513.17, $860.33) B) ($238.23, $326.41)

C) ($326.21, $437.90) D) ($487.31, $563.80)

43) When 475 college students were surveyed, 125 said they own their car. Find a point estimate for p, the population proportion of students who own their cars. 43) _______

A) 0.263 B) 0.737 C) 0.357 D) 0.208

44) A survey of 100 fatal accidents showed that 11 were alcohol related. Find a point estimate for p, the population proportion of accidents that were alcohol related. 44) _______

A) 0.11 B) 0.89 C) 0.124 D) 0.099

45) A survey of 500 non-fatal accidents showed that 118 involved the use of a cell phone. Find a point estimate for p, the population proportion of accidents that involved the use of a cell phone. 45) _______

A) 0.236 B) 0.764 C) 0.309 D) 0.191

46) A survey of 250 households showed 37 owned at least one gun. Find a point estimate for p, the population proportion of households that own at least one gun. 46) _______

A) 0.148 B) 0.852 C) 0.174 D) 0.129

47) A survey of 2490 golfers showed that 347 of them are left-handed. Find a point estimate for p, the population proportion of golfers that are left-handed. 47) _______

A) 0.139 B) 0.861 C) 0.162 D) 0.122

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

48) When 385 college students were surveyed, 160 said they own their car. Construct a 95% confidence interval for the proportion of college students who say they own their cars. 48) _____________

49) A survey of 600 non-fatal accidents showed that 166 involved the use of a cell phone. Construct a 99% confidence interval for the proportion of fatal accidents that involved the use of a cell phone. 49) _____________

50) A survey of 100 fatal accidents showed that 52 were alcohol related. Construct a 98% confidence interval for the proportion of fatal accidents that were alcohol related. 50) _______

A) (0.404, 0.636) B) (0.120, 0.340)

C) (0.560, 0.580) D) (0.880, 0.900)

51) A survey of 250 households showed 62 owned at least one gun. Construct a 90% confidence interval for the proportion of households that own at least one gun. 51) _______

A) (0.203, 0.293) B) (0.103, 0.189)

C) (0.369, 0.451) D) (0.683, 0.712)

52) A survey of 2450 golfers showed that 281 of them are left-handed. Construct a 98% confidence interval for the proportion of golfers that are left-handed. 52) _______

A) (0.100, 0.130) B) (0.203, 0.293)

C) (0.369, 0.451) D) (0.683, 0.712)