# MATHEMATICS

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

Solve the problem.

1)  A random sample of  700 high school seniors is given the SAT-V test. The mean score for this sample is  overbar(x) = 487. What can you say about the mean score m of all high school seniors? 1)  ______________

2)  The grade point averages for 10 randomly selected students in a statistics class with 125 students are listed below. What can you say about the mean score m of all 125 students?

3.7     2.5     2.3     2.0     2.6     3.5     2.1     2.8     2.4     3.6 2)  ______________

3)  A certain confidence in interval is  8.35 < m <  9.85. Find the sample mean  overbar(x) and the error of estimate E. 3)  ______________

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

4)  Given the same sample statistics, which level of confidence will produce the narrowest confidence interval? 4)  ________

A) 75% B)  85% C)  90% D)  95%

5)  The grade point averages for 10 randomly selected students in a statistics class with 125 students are listed below.

2.0    3.2    1.8    2.9    0.9    4.0    3.3    2.9    3.6    0.8

What is the effect on the width of the confidence interval if the sample size is increased to 20? 5)  ________

A) The width decreases.

B) The width increases.

C) The width remains the same.

6)  Find the critical value  _elementsubscript_element that corresponds to a  94% confidence level. 6)  ________

A)  plusminus1.88 B)   plusminus1.645 C)   plusminus1.96 D)   plusminus2.33

7)  Determine the error of estimate if the grade point averages for 10 randomly selected students from a class of 125 students has a mean of  overbar(x) =  2.0. Assume the grade point average of the 125 students has a mean of m =  2.5. 7)  ________

A)  0.5 B)   2.25 C)  – 0.5 D)   1.75

8)  A random sample of  50 students has a test score average with a standard deviation of  11.4. Find the maximum error of estimate if c =  0.98. 8)  ________

A)  3.76 B)   0.53 C)   1.61 D)   1.58

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

9)  In a recent study of  71 eighth graders, the mean number of hours per week that they watched television was  18.7 with a standard deviation of  5.8 hours.

a) Find the  98% confidence interval of the mean.

b) If the standard deviation is doubled to  11.6, what will be the effect on the confidence interval? 9)  ______________

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)  _____________

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