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3/21/2019 Chapter 6 Test-Abraham Haje

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Student: _____________________ Date: _____________________

Instructor: Abraham Haje Course: Math 1342 Statistics T TH12:30PM-1:50PM

Assignment: Chapter 6 Test

Find the critical value that corresponds to a % confidence level.zc 98

A. ± 2.33B. ± 1.645C. ± 2.575D. ± 1.96

Determine the sampling error if the grade point averages for 10 randomly selected students from a class of 125 students has a mean of . Assume the grade point average of the 125 students has a mean of x = 2.1 μ = 2.9.

A. 1.7B. 2.5C. − 0.08D. − 0.8

The grade point average collected from a random sample of 150 students. Assume that the population standard deviation is 0.78. Find the margin of error if c 0.98.=

A. 0.08B. 0.15C. 0.11D. 0.12

A random sample of 40 students has a mean annual earnings of $3120 and assume that the population standard deviation is $677. Find the margin of error if c 0.95.=

A. $77B. $7C. $210D. $2891

The grade point average collected from a random sample of 150 students producing a mean of 2.86. Assume that the population standard deviation is 0.78. Construct the confidence interval for the population mean, , if c 0.98.μ =

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



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A random sample of 40 students has a mean annual earnings of $3120 and assume that the population standard deviation is $677. Construct the confidence interval for the population mean, if μ c = 0.95.

A. ($1987,$2346)B. ($2910,$3330)C. ($4812,$5342)D. ($210,$110)

A random sample of 56 fluorescent light bulbs has a mean life of 645 hours and assume that the population standard deviation is 31 hours. Construct a 95% confidence interval for the population mean.

A. (539.6,551.2)B. (636.9,653.1)C. (112.0,118.9)D. (712.0,768.0)

A group of 49 randomly selected students has a mean age of 22.4 years and assume that the population standard deviation is 3.8. Construct a 98% confidence interval for the population mean.

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

In a random sample of 60 computers, the mean repair cost was $150 and assume that the population standard deviation is $36. Construct a 90% confidence interval for the population mean.

A. ($138,$162)B. ($537,$654)C. ($141,$159)D. ($142,$158)

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

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

In a sample of 10 randomly selected women, it was found that their mean height was 63.4 inches. From previous studies, it can be assumed that the population standard deviation is 2.4 and that the population of height measurements is normally distributed. Construct the 95% confidence interval for the population mean.

σ

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



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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 % confident that the true mean is within ounces of the sample mean? The population standard deviation of the birth weights is known to be ounces.

90 37

A. 4B. 3C. 15D. 14

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 population standard deviation is 2.8 days. 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?

A. 141B. 512C. 1024D. 31

In order to efficiently bid on a contract, a contractor wants to be 95% confident that his error is less than two hours in estimating the average time it takes to install tile flooring. Previous contracts indicate that the population standard deviation is 4.5 hours. How large a sample must be selected?

A. 4B. 5C. 20D. 19

Find the critical value, for c 0.99 and n 10.tc = =

A. 3.169B. 3.250C. 2.262D. 1.833

Find the critical value, , for c 0.95 and n 16.tc = =

A. 2.120B. 2.602C. 2.131D. 2.947

Find the critical value, , for c 0.90 and n 15.tc = =

A. 2.624B. 2.145C. 1.761D. 1.753



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Find the value of E, the margin of error, for c 0. , n 10 and s .= 90 = = 3.7

A. 2.12B. 0.678C. 2.145D. 1.618

Find the value of E, the margin of error, for c 0. , n 15 and s .= 90 = = 5.4

A. 1.875B. 2.455C. 0.634D. 2.53

In a random sample of 28 families, the average weekly food expense was $95.60 with a standard deviation of $22.50. Determine whether a normal distribution or a t-distribution should be used or whether neither of these can be used to construct a confidence interval. Assume the distribution of weekly food expenses is normally shaped.

A. Use the t-distribution.B. Use normal distribution.C. Cannot use normal distribution or t-distribution.

A random sample of 40 college students has a mean earnings of $3120 over the summer months. Assume the population standard deviation of earnings over the summer months for college students is $677 and that the distribution of earnings over the summer months for college students is normally distributed. Determine whether a normal distribution or a t-distribution should be used or whether neither of these can be used to construct a confidence interval.

A. Use a normal distribution.B. Use a t-distribution.C. Cannot use a normal distribution or a t-distribution.

A random sample of 15 statistics textbooks has a mean price of $105 with a standard deviation of $30.25. Determine whether a normal distribution or a t-distribution should be used or whether neither of these can be used to construct a confidence interval. Assume the distribution of statistics textbook prices is not normally distributed.

A. Cannot use normal distribution or t-distribution.B. Use normal distribution.C. Use the t-distribution.

Construct a 95% confidence interval for the population mean, . 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.

μ

A. ($2135,$2567)B. ($1324,$1567)C. ($2657,$2891)D. ($2803,$3437)



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Construct a 95% confidence interval for the population mean, . 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.

μ

A. (66.35,69.89)B. (77.29,85.71)C. (87.12,98.32)D. (56.12,78.34)

Construct a 95% confidence interval for the population mean, . 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.

μ

A. (876.2,981.5)B. (321.7,365.8)C. (628.5,661.5)D. (531.2,612.9)

Construct a 99% confidence interval for the population mean, . 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.

μ

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

Construct a 90% confidence interval for the population mean, . 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.

μ

A. (18.63,20.89)B. (19.62,23.12)C. (5.87,7.98)D. (17.47,21.73)

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.

A. ($3.39,$6.01)B. ($1.35,$2.85)C. ($2.11,$5.34)D. ($4.81,$6.31)



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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.

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

Determine the point estimate of the population mean and margin of error for the confidence interval with lower bound of and upper bound of .21 39

A. , Ex = 21 = 18B. , Ex = 30 = 9C. , Ex = 30 = 18D. , Ex = 39 = 9

Construct a 99% confidence interval for the population mean, . Assume the population has a normal distribution. A group of 19 randomly selected employees has a mean age of 22.4 years with a standard deviation of 3.8 years. Round to the nearest tenth.

μ

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

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

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A. 0.72B. 0.218C. 0.388D. 0.28

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

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A. 0.41B. 0.291C. 0.695D. 0.59



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

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A. 0.206B. 0.74C. 0.351D. 0.26

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

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A. 0.192B. 0.161C. 0.139D. 0.839

In a survey of 2480 golfers, 15% said they were left-handed. The survey's margin of error was 3%. Construct a confidence interval for the proportion of left-handed golfers.

A. (0.12,0.15)B. (0.12,0.18)C. (0.11,0.19)D. (0.18,0.21)

A survey of 280 homeless persons showed that 63 were veterans. Construct a 90% confidence interval for the proportion of homeless persons who are veterans.

A. (0.161,0.289)B. (0.176,0.274)C. (0.167,0.283)D. (0.184,0.266)

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 % confident that the sample proportion will not differ from the true proportion by more than %?

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A. 752B. 17C. 2,135D. 1,068

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 % confident that the sample proportion will not differ from the true proportion by more than %?90 4

A. 11B. 423C. 256D. 846



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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 % confident that the sample proportion will not differ from the true proportion by more than %?

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A. 543B. 385C. 1,086D. 12

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

indicates that the proportion of households with two cars is %.90 2

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A. 1,489B. 1,161C. 2D. 703

Find the critical values, and , for c 0.95 and n 12. X2R X2

L = =

A. 2.603 and 19.675B. 3.053 and 24.725C. 4.575 and 26.757D. 3.816 and 21.920

Find the critical values, and , for c 0.90 and n 15.X2R X2

L = =


Find the critical values, and , for c 0.99 and n 10.X2R X2

L = =


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

σ

10.5

A. ( , )8.073 15.326B. ( , )7.687 16.559C. ( , )59.095 274.205D. ( , )2.372 5.11



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A random sample of 16 men have a mean height of 67.5 inches and a standard deviation of inches. Construct a 99% confidence interval for the population standard deviation, .

1.3σ

A. ( , )0.911 2.202B. ( , )0.771 2.059C. ( , )0.879 2.347D. ( , )0.908 2.424

The heights (in inches) of 20 randomly selected adult males are listed below. Construct a 99% confidence interval for the variance, . σ

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70 72 71 70 69 73 69 68 70 7167 71 70 74 69 68 71 71 71 72

A. (2.16,71.06)B. (1.35,8.43)C. (1.47,8.27)D. (21.61,69.06)

The grade point averages for 10 randomly selected students are listed below. Construct a 90% confidence interval for the population standard deviation, . σ

2.0, 3.2, 1.8, 2.9, 0.9, 4.0, 3.3, 2.9, 3.6, 0.8

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

The mean replacement time for a random sample of 12 microwave ovens is 8.6 years with a standard deviation of years. Construct the 98% confidence interval for the population variance, .

4.4σ

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A. ( , )1.958 15.853B. ( , )2.935 8.352C. ( , )8.123 59.636D. ( , )8.613 69.754

The stem-and-leaf plot shows the test scores of 16 randomly selected students. Construct a 99% confidence interval for the population standard deviation.

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3 1 7

A. (62.18,363.63)B. (7.89,19.07)C. (57.97,413.27)D. (7.61,20.33)



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The dotplot shows the weights (in pounds) of 15 dogs selected randomly from those adopted out by an animal shelter last week. Construct a 98% confidence interval for the population variance.

Weights

Pounds

A. (2.89,16.91)B. (3.38,15.70)C. (1.74,4.36)D. (3.03,18.97)

Construct the indicated confidence intervals for the population variance and the population standard deviation . Assume the sample is from a normally distributed population.

σ2

σ

c 0.95, , n 25= s2 = 15.10 =

A. Confidence interval for : ( , ); Confidence interval for : ( , )σ2 8.92 27.62 σ 2.99 5.26

B. Confidence interval for : ( , ); Confidence interval for : ( , )σ2 9.62 24.80 σ 3.10 4.98

C. Confidence interval for : ( , ); Confidence interval for : ( , )σ2 9.21 29.22 σ 3.03 5.41

D. Confidence interval for : ( , ); Confidence interval for : ( , )σ2 13.72 26.17 σ 3.70 5.12

Construct the indicated confidence intervals for the population variance and the population standard deviation . Assume the sample is from a normally distributed population.

σ2

σ

c 0.99, s , n 61= = 238.9 =

A. Confidence interval for : ( , ); Confidence interval for : ( , )σ2 43,301.80 79,290.37 σ 208.09 281.59

B. Confidence interval for : ( , ); Confidence interval for : ( , )σ2 46,028.64 73,707.84 σ 214.54 271.49

C. Confidence interval for : ( , ); Confidence interval for : ( , )σ2 37,241.09 96,369.47 σ 192.98 310.43

D. Confidence interval for : ( , ); Confidence interval for : ( , )σ2 41,110.14 84,590.50 σ 202.76 290.84

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

σ

13.5

A. ( , )97.688 453.278B. ( , )9.884 21.29C. ( , )10.379 19.705D. ( , )2.69 5.794

A random sample of 16 men have a mean height of 67.5 inches and a standard deviation of inches. Construct a 99% confidence interval for the population standard deviation, . Assume the sample is from a normally distributed population.

1.3σ

A. ( , )0.771 2.059B. ( , )0.911 2.202C. ( , )0.908 2.424D. ( , )0.879 2.347

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A random sample of 20 women have a mean height of 62.5 inches and a standard deviation of inches. Construct a 98% confidence interval for the population variance, . Assume the sample is from a normally distributed population.

2.5σ

2

A. ( , )3.281 15.557B. ( , )1.811 3.944C. ( , )1.312 6.223D. ( , )3.454 16.376

The heights (in inches) of 20 randomly selected adult males are listed below. Construct a 99% confidence interval for the variance, . Assume the sample is from a normally distributed population.σ

2

70 72 71 70 69 73 69 68 70 7167 71 70 74 69 68 71 71 71 72

A. (1.47, 8.27)B. (1.35, 8.43)C. (2.16, 71.06)D. (21.61, 69.06)

The grade point averages for 10 randomly selected students are listed below. Construct a 90% confidence interval for the population standard deviation, . Assume the sample is from a normally distributed population.σ

2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8

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

The mean replacement time for a random sample of 12 microwave ovens is 8.6 years with a standard deviation of years. Construct the 98% confidence interval for the population variance, . Assume the sample is from a normally distributed population.

2.4σ

2

A. ( , )2.417 17.743B. ( , )2.563 20.753C. ( , )1.601 4.556D. ( , )1.068 8.647

A student randomly selects 10 CDs at a store. The mean is $13.75 with a standard deviation of $1.50. Construct a 95% confidence interval for the population standard deviation, . Assume the sample is from a normally distributed population.σ

A. ($0.84, $2.24)B. ($1.06, $7.51)C. ($1.03, $2.74)D. ($0.99, $2.50)



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The stem-and-leaf plot shows the test scores of 16 randomly selected students. Construct a 99% confidence interval for the population standard deviation. Assume the sample is from a normally distributed population.

Key: 2 525 =

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5 8 3

7 4 4 2 9

5 8 3 5

3 1 7

A. (57.97, 413.27)B. (7.89, 19.07)C. (62.18, 363.63)D. (7.61, 20.33)

The dotplot shows the weights (in pounds) of 15 dogs selected randomly from those adopted out by an animal shelter last week. Construct a 98% confidence interval for the population variance. Assume the sample is from a normally distributed population.

Weights

35 40 45 50 55 60 65 70 75 80 85 Pounds

A. ( , )84.5 392.5B. ( , )72.25 422.75C. ( , )43.5 109D. ( , )75.75 474.25



1. A. ± 2.33

2. D. − 0.8

3. B. 0.15

4. C. $210

5. D. (2.71,3.01)

6. B. ($2910,$3330)

7. B. (636.9,653.1)

8. B. (21.1,23.7)

9. D. ($142,$158)

10. A. (17.5,21.7)

11. C. (61.9,64.9)

12. C. 15

13. D. 31

14. C. 20

15. B. 3.250

16. C. 2.131

17. C. 1.761

18. C. 2.145



19. B. 2.455

20. A. Use the t-distribution.

21. A. Use a normal distribution.

22. A. Cannot use normal distribution or t-distribution.

23. D. ($2803,$3437)

24. B. (77.29,85.71)

25. C. (628.5,661.5)

26. B. (19.9,24.9)

27. D. (17.47,21.73)

28. A. ($3.39,$6.01)

29. A. (1.55,3.53)

30. B. , Ex = 30 = 9

31. C. (19.9,24.9)

32. D. 0.28

33. A. 0.41

34. D. 0.26

35. B. 0.161

36. B. (0.12,0.18)



37. D. (0.184,0.266)

38. D. 1,068

39. B. 423

40. A. 543

41. B. 1,161

42. D. 3.816 and 21.920

43. D. 6.571 and 23.685

44. A. 1.735 and 23.587

45. B. ( , )7.687 16.559

46. C. ( , )0.879 2.347

47. C. (1.47,8.27)

48. D. (0.81,1.83)

49. D. ( , )8.613 69.754

50. D. (7.61,20.33)

51. D. (3.03,18.97)

52. C. Confidence interval for : ( , ); Confidence interval for : ( , )σ2 9.21 29.22 σ 3.03 5.41

53. C. Confidence interval for : ( , ); Confidence interval for : ( , )σ2 37,241.09 96,369.47 σ 192.98 310.43

54. B. ( , )9.884 21.29



55. D. ( , )0.879 2.347

56. A. ( , )3.281 15.557

57. A. (1.47, 8.27)

58. A. (0.81, 1.83)

59. B. ( , )2.563 20.753

60. C. ($1.03, $2.74)

61. D. (7.61, 20.33)

62. D. ( , )75.75 474.25

(2.71,3.01) - houston community college

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