Mar 31, 2017

Estimates and Sample Sizes — practice test 7B

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 98%.
      1. 2.05
      2. 1.75
      3. 2.33
      4. 2.575

    • 2. The following confidence interval is obtained for a population proportion, p:
      (0.870, 0.897)
      Use these confidence interval limit to find the point estimate, p̂.
      1. 0.882
      2. 0.885
      3. 0.870
      4. 0.894

  • Find the margin of error for the 95% confidence interval used to estimate the population proportion.
    • 3. In a clinical test with 2440 subjects, 70% showed improvement from the treatment.
      1. 0.0196
      2. 0.0236
      3. 0.0182
      4. 0.0175

  • Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
    • 4. n = 107, x = 66; 88 percent
      1. 0.539 < p < 0.695
      2. 0.540 < p < 0.694
      3. 0.543 < p < 0.691
      4. 0.544 < p < 0.690

  • Find the minimum sample size you should use to assure that your estimate of p̂ will be within the required margin of error the population p.
    • 5. Margin of error: 0.07; confidence level: 97%, p̂ and q̂ are unknown.
      1. 240
      2. 241
      3. 111
      4. 112

    • 6. Margin of error: 0.008; confidence level: 99%; from a prior study, p̂ is estimated by 0.164.
      1. 12,785
      2. 8230
      3. 14,205
      4. 1145

  • Solve the problem.
    • 7. 38 randomly picked people were asked if they rented or owned their own home, 11 said they rented. Obtain a point estimate of the true proportion of home owners.
      1. 0.737
      2. 0.289
      3. 0.711
      4. 0.224

  • Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
    • 8. A survey of 300 union members in New York State reveals that 112 favor the Republican candidate for governor. Construct the 98% confidence interval for the true population proportion of all New York State union members who favor the Republican candidate.
      1. 0.308 < p < 0.438
      2. 0.304 < p < 0.442
      3. 0.316 < p < 0.430
      4. 0.301 < p < 0.445

  • Solve the problem.
    • 9. A one-sided confidence interval for p can be written as p < p̂ + E or p > p̂ - E where the margin of error E is modified by replacing zα/2 with zα. If a teacher wants to report that the fail rate on a test is at most x with 90% confidence, construct the appropriate one-sided confidence interval. Assume that a simple random sample of 58 students results in 6 who fail the test.
      1. p > 0.155
      2. p > 0.052
      3. p < 0.052
      4. p < 0.155

  • 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 = 8, and σ is not known.
      1. Yes
      2. No

  • Use the confidence level and sample data to find the margin of error E.
    • 11. College students’ annual earnings: 99% confidence; n = 66, x̅ = $3903, σ = $801.
      1. $254
      2. $8
      3. $230
      4. $1237

  • Use the confidence level and sample data to find a confidence interval for estimation the population μ.
    • 12. A random sample of 100 full-grown lobsters had a mean weight of 22 ounces and a standard deviation of 3.7 ounces. Construct a 98 percent confidence interval for the population mean μ.
      1. 22 < μ < 24
      2. 21 < μ < 23
      3. 20 < μ < 22
      4. 21 < μ < 24

  • 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: $136, confidence level: 99%, σ = $503.
      1. 91
      2. 53
      3. 10
      4. 46

  • 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. 90%; n = 9; σ = 4.2; population appears to be very skewed.
      1. zα/2 = 2.896
      2. Neither the normal nor the t distribution applies.
      3. zα/2 = 2.306
      4. zα/2 = 2.365

  • Find the margin of error.
    • 15. 95% confidence interval; n = 12; x̅ = 35.6; s = 6.4.
      1. 4.066
      2. 3.659
      3. 3.050
      4. 4.879

  • 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 amount (in ounces) of juice in eight randomly selected juice bottles are:
      15.1 15.6 15.6 15.9
      15.9 15.2 15.1 15.2
      Construct a 98 percent confidence interval for the mean amount of juice in all such bottles.
      1. 15.77 < μ < 15.13
      2. 15.09 < μ < 15.81
      3. 15.03 < μ < 15.87
      4. 15.87 < μ < 15.03

  • Solve the problem.
    • 17. Find the critical value X2L corresponding to a sample size of 3 and a confidence level of 90 percent.
      1. 5.991
      2. 9.21
      3. 0.103
      4. 0.0201

  • 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. Weights of men: 90% confidence; n = 14, x̅ = 156.9 lb, s = 11.1 lb.
      1. 9.0 lb < σ < 2.7 lb
      2. 8.5 lb < σ < 16.5 lb
      3. 8.7 lb < σ < 14.3 lb
      4. 8.2 lb < σ < 15.6 lb

  • Find the appropriate minimum sample size.
    • 19. To be able to say with 95% confidence level that the standard deviation of a data set is within 10% of the population’s standard deviation, the number of observations within the data set must be greater than or equal to what quantity?
      1. 191
      2. 805
      3. 335
      4. 250

  • 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 amounts (in ounces) of juice in eight randomly selected juice bottles are:
      15.8 15.7 15.0 15.7
      15.2 15.2 15.5 15.0
      Find a 98 percent confidence interval for the population standard deviation σ.
      1. (0.20, 0.78)
      2. (0.20, 0.67)
      3. (0.19, 0.67)
      4. (0.22, 0.84)

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