Mathematics short answer

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.

D) It is impossible to tell without more information.

 

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)  _____________

 

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

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)  _____________

 

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

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)

 

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

53)  In a survey of 10 golfers, 2 were found to be left-handed. Is it practical to construct the 90% confidence interval for the population proportion, p? Explain.

 

53)  _____________

 

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

54)  A researcher at a major hospital wishes to estimate the proportion of the adult population of the United States that has high blood pressure. How large a sample is needed in order to be  98% confident that the sample proportion will not differ from the true proportion by more than  6%? 54)  _______

A)  378 B)   10 C)   755 D)   267

 

55)  A pollster wishes to estimate the proportion of United States voters who favor capital punishment. How large a sample is needed in order to be  90% confident that the sample proportion will not differ from the true proportion by more than  4%? 55)  _______

A)  423 B)   256 C)   11 D)   846

 

56)  A private opinion poll is conducted for a politician to determine what proportion of the population favors decriminalizing marijuana possession. How large a sample is needed in order to be  95% confident that the sample proportion will not differ from the true proportion by more than  3%? 56)  _______

A)  1068 B)   752 C)   2135 D)   17

 

57)  A manufacturer of golf equipment wishes to estimate the number of left-handed golfers. How large a sample is needed in order to be  99% confident that the sample proportion will not differ from the true proportion by more than  6%? A previous study indicates that the proportion of left-handed golfers is  10%. 57)  _______

A)  166 B)   136 C)   185 D)   38

 

58)  A researcher wishes to estimate the number of households with two cars. How large a sample is needed in order to be  95% confident that the sample proportion will not differ from the true proportion by more than  5%? A previous study indicates that the proportion of households with two cars is  24%. 58)  _______

A)  281 B)   198 C)   369 D)   4

 

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

59)  A state highway patrol official wishes to estimate the number of drivers that exceed the speed limit traveling a certain road.

a) How large a sample is needed in order to be  90% confident that the sample proportion will not differ from the true proportion by more than  2%?

b) Repeat part (a) assuming previous studies found that  85% of drivers on this road exceeded the speed limit. 59)  _____________

 

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

60)  Find the critical values,  X with (superscript (stacked) and subscript (~%3)) and X with (superscript (stacked) and subscript (~%3)), for c = 0.95 and n = 12.    60)  _______

A) 3.816 and 21.920 B)  3.053 and 24.725

C) 4.575 and 26.757 D)  2.603 and 19.675

 

61)  Find the critical values,  X with (superscript (stacked) and subscript (~%3)) and X with (superscript (stacked) and subscript (~%3)), for c = 0.90 and n = 15. 61)  _______

A) 6.571 and 23.685 B)  4.075 and 31.319

C) 4.660 and 29.131 D)  5.629 and 26.119

 

62)  Find the critical values,  X with (superscript (stacked) and subscript (~%3)) and X with (superscript (stacked) and subscript (~%3)), for c = 0.98 and n = 20. 62)  _______

A) 7.633 and 36.191 B)  6.844 and 27.204

C) 8.907 and 38.582 D)  10.117 and 32.852

 

63)  Find the critical values,  X with (superscript (stacked) and subscript (~%3)) and X with (superscript (stacked) and subscript (~%3)), for c = 0.99 and n = 10. 63)  _______

A) 1.735 and 23.587 B)  2.156 and 25.188

C) 2.088 and 21.666 D)  2.558 and 23.209

 

64)  Construct a 95% confidence interval for the population standard deviation s of a random sample of 15 men who have a mean weight of 165.2 pounds with a standard deviation of  12.4 pounds. Assume the population is normally distributed. 64)  _______

A) ( 9.1,  19.6) B)  ( 82.4,  382.4) C)  ( 2.6,  5.6) D)  ( 9.5,  18.1)

 

65)  Assume that the heights of men are normally distributed. A random sample of 16 men have a mean height of 67.5 inches and a standard deviation of  2.6 inches. Construct a 99% confidence interval for the population standard deviation, s. 65)  _______

A) ( 1.8,  4.7) B)  ( 1.8,  4.8) C)  ( 1.1,  2.9) D)  ( 1.8,  4.4)

 

66)  Assume that the heights of women are normally distributed. A random sample of 20 women have a mean height of 62.5 inches and a standard deviation of  1.4 inches. Construct a 98% confidence interval for the population variance,  sigma to power of (2). 66)  _______

A) ( 1.0,  4.9) B)  ( 1.0,  2.2) C)  ( 0.7,  3.5) D)  ( 1.1,  5.1)

 

67)  The mean replacement time for a random sample of 12 microwave ovens is 8.6 years with a standard deviation of  2.7 years. Construct the 98% confidence interval for the population variance,  sigma to power of (2). Assume the data are normally distributed 67)  _______

A) ( 3.2,  26.3) B)  ( 1.8,  5.1) C)  ( 1.2,  9.7) D)  ( 3.1,  22.5)

 

68)  A student randomly selects 10 CDs at a store. The mean is $8.75 with a standard deviation of $1.50. Construct a 95% confidence interval for the population standard deviation, s. Assume the data are normally distributed. 68)  _______

A) ($1.03, $2.74) B)  ($0.43, $1.32)

C) ($1.43, $2.70) D)  ($1.76, $3.10)

 

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

69)  The heights (in inches) of 20 randomly selected adult males are listed below. Construct a 99% confidence interval for the variance,  sigma to power of (2). Assume the population is normally distributed.

 

70    72    71    70    69    73    69    68    70    71

67    71    70    74    69    68    71    71    71    72 69)  _____________

 

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

70)  The grade point averages for 10 randomly selected students are listed below. Construct a 90% confidence interval for the population standard deviation, s. Assume the data are normally distributed.

 

2.0    3.2    1.8    2.9    0.9    4.0    3.3    2.9    3.6    0.8 70)  _______

A) (0.81, 1.83) B)  (0.32, 0.85) C)  (0.53, 1.01) D)  (1.10, 2.01)

 

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

71)  A container of car oil is supposed to contain 1000 milliliters of oil. A quality control manager wants to be sure that the standard deviation of the oil containers is less than 20 milliliters. He randomly selects 10 cans of oil with a mean of 997 milliliters and a standard deviation of 32 milliliters. Use these sample results to construct a 95% confidence interval for the true value of s. Does this confidence interval suggest that the variation in the oil containers is at an acceptable level? 71)  _____________