Mar 31, 2017

# Estimates and Sample Sizes — practice test 7C

20 cards
Problems with solutions in Elementary Statistics — Estimating a Population Proportion, Estimating a Population Mean: σ Known, Estimating a Population Mean: σ Not Known, Estimating a Population Variance.

Directions:
Choose the correct answer for multiple-choice items.

• Solve the problem.
• 1. Find the critical value of zα/2 that corresponds to a degree of confidence of 91%.
1. 1.34
2. 1.70
3. 1.75
4. 1.645

• 2. The following confidence interval is obtained for a population proportion, p:
0.817 < p < 0.855
Use these confidence interval limit to find the point estimate, p̂.
1. 0.817
2. 0.833
3. 0.836
4. 0.839

• Find the margin of error for the 95% confidence interval used to estimate the population proportion.
• 3. n = 186, x = 103
1. 0.0714
2. 0.00260
3. 0.0643
4. 0.125

• Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
• 4. n = 158, x = 108; 95 percent
1. 0.611 < p < 0.756
2. 0.610 < p < 0.758
3. 0.625 < p < 0.743
4. 0.626 < p < 0.742

• Find the minimum sample size you should use to assure that your estimate of p̂ will be within the required margin of error around the population p.
• 5. Margin of error: 0.002; confidence level: 93%, p̂ and q̂ are unknown.
1. 410
2. 405
3. 204,757
4. 204,750

• 6. Margin of error: 0.07; confidence level: 95%; from a prior study, p̂ is estimated by the decimal equivalent of 92%.
1. 4
2. 51
3. 174
4. 58

• Solve the problem.
• 7. 61 randomly selected light bulbs were tested in a laboratory, 50 lasted more than 500 hours. Find a point estimate of the true proportion of all light bulbs that last more than 500 hours.
1. 0.803
2. 0.180
3. 0.450
4. 0.820

• Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
• 8. When 343 college students are randomly selected and surveyed, it is found that 110 own a car. Find a 99% confidence interval for the true proportion of all college students who own a car.
1. 0.256 < p < 0.386
2. 0.279 < p < 0.362
3. 0.271 < p < 0.370
4. 0.262 < p < 0.379

• Solve the problem.
• 9. A researcher is interested in estimation the proportion of voters who favor a tax on e-commerce. Based on a sample of 260 people, she obtains the following 99% confidence interval for the population proportion p:
0.113 < p < 0.171.

Which of the statements below is a valid interpretation of this confidence interval?
A: There is a 99% chance that the true value of p lies between 0.113 and 0.171.
B: If many different samples of size 250 were selected and, based on each sample, a confidence interval were constructed, 99% of the time the true value of p would lie between 0.113 and 0.171.
C: If many different samples of size 250 were selected and, based on each sample, a confidence interval were constructed, in the long run 99% of the confidence intervals would contain the true value of p.
D: If 100 different samples of size 250 were selected and, based on each sample, a confidence interval were constructed, exactly 99 of these confidence intervals would contain the true value of p.
1. D
2. C
3. B
4. A

• Determine whether the given conditions justify using the margin of error E = zα/2 σ/ √n when finding a confidence interval estimate of the population mean μ.
• 10. The sample size is n = 9, and σ is not known, and the original population is normally distributed.
1. No
2. Yes

• Use the confidence level and sample data to find the margin of error E.
• 11. Systolic blood pressures for women aged 18–24: 94% confidence; n = 92, x̅ = 114.9 mm Hg, σ = 13.2 mm Hg.
1. 9.6 mm Hg
2. 47.6 mm Hg
3. 2.3 mm Hg
4. 2.6 mm Hg

• Use the confidence level and sample data to find a confidence interval for estimation the population μ.
• 12. A group of 52 randomly selected students have a mean sore of 20.2 with a standard deviation of 4.6 on a placement test. What is the 90 percent confidence interval for the mean score, μ, of all students taking the test.
1. 18.7 < μ < 21.7
2. 19.0 < μ < 21.5
3. 18.6 < μ < 21.8
4. 19.1 < μ < 21.3

• Use the margin of error, confidence level, and standard deviation σ to find the minimum sample size required to estimate an unknown population mean μ.
• 13. Margin of error: \$100, confidence level: 95%, σ = \$403.
1. 91
2. 44
3. 108
4. 63

• Do one of the following, as appropriate:
(a) Find the critical value zα/2;
(b) Find the critical value tα/2;
(c) State that neither the normal nor the t distribution applies.
• 14. 99%; n = 17; σ is unknown; population appears to be normally distributed.
1. zα/2 = 2.583
2. zα/2 = 2.921
3. zα/2 = 2.567
4. zα/2 = 2.898

• Find the margin of error.
• 15. 99% confidence interval; n = 201; x̅ = 175; s = 21.
1. 6.0
2. 4.6
3. 8.2
4. 3.9

• Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution.
• 16. The football coach randomly selected ten players and timed how long each player took to perform a certain drill. The times (in minutes) were:
7.6 10.4 9.7 8.4 11.8
7.0 6.5 11.1 10.4 12.4
Determine a 95 percent confidence interval for the mean time for all players.
1. 8.00 < μ < 10.98
2. 8.13 < μ < 10.93
3. 8.03 < μ < 11.03
4. 8.06 < μ < 11.00

• Solve the problem.
• 17. Find the critical value X2L corresponding to a sample size of 15 and a confidence level of 90 percent.
1. 31.319
2. 23.685
3. 29.141
4. 21.064

• Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ. Assume that the population has a normal distribution.
• 18. College students’ annual earnings: 90% confidence; n = 9, x̅ = \$3605, s = \$800.
1. \$629 < σ < \$1044
2. \$505 < σ < \$1764
3. \$486 < σ < \$1566
4. \$540 < σ < \$1533

• Find the appropriate minimum sample size.
• 19. You want to be 95% confident that the sample variance is within 40% of the population variance.
1. 14
2. 11
3. 56
4. 224

• Use the give degree of confidence and sample data to find a confidence interval for the population standard deviation σ. Assume that the population has a normal distribution.
• 20. The football coach randomly selected ten players and timed how long each player took to perform a certain drill. The times (in minutes) were:
7 12 10 14 10
14 9 11 7 14
Find a 95 percent confidence interval for the population standard deviation σ.
1. (0.7, 2.2)
2. (1.8, 4.5)
3. (1.9, 4.5)
4. (1.9, 4.9)