Mar 31, 2017

Estimates and Sample Sizes — practice test 7C

20 cards
, 78 answers
    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)

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