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)

© 2017 DrillPal.com