Chapter 6 Test - Mathematics for College Statistics

Which statistic is the best unbiased estimator for μ? The best unbiased estimated for μ is (1) X̄. ○ the mode. ○ the median. ○ s.

• X̄
• the mode

• the median

• s

For the same sample statistics, which level of confidence would produce the widest confidence interval? Explain your reasoning. Choose the correct answer below.

• 99%, because as the level of confidence increases, z_c decreases.

• 99%, because as the level of confidence increases, z_c increases.

• 90%, because as the level of confidence decreases, z_c decreases.

• 90%, because as the level of confidence decreases, z_c increases.

Find the margin of error for the given values of c, σ, and n. c = 0.90, σ = 2.8, n = 100. E = ________ (Round to three decimal places as needed.)

• E = 0.460

• E = 0.560

• E = 0.660

• E = 0.760

Find the margin of error for the given values of c, σ, and n. c = 0.90, σ = 2.3, n = 49. Click the icon to view a table of common critical values. E = ________ (Round to three decimal places as needed.)

• E = 0.643

• E = 0.721

• E = 0.512

• E = 0.589

Construct the confidence interval for the population mean μ. Given: c = 0.98, x̄ = 7.9, σ = 0.3, and n = 51. A 98% confidence interval for μ is (______, ______). (Round to two decimal places as needed.)

• A 98% confidence interval for μ is (7.80, 8.00).

• A 98% confidence interval for μ is (7.85, 7.95).

• A 98% confidence interval for μ is (7.70, 8.10).

• A 98% confidence interval for μ is (7.75, 8.05).

Construct the confidence interval for the population mean μ. Given: c = 0.95, x̄ = 15.8, σ = 9.0, and n = 75. A 95% confidence interval for μ is (______, ______). (Round to one decimal place as needed.)

• A 95% confidence interval for μ is (13.8, 17.8).

• A 95% confidence interval for μ is (14.0, 17.6).

• A 95% confidence interval for μ is (15.0, 16.6).

• A 95% confidence interval for μ is (12.5, 19.1).

• A. With 90% confidence, it can be said that the population mean price lies in the first interval. With 95% confidence, it can be said that the population mean price lies in the second interval. The 95% confidence interval is wider than the 90%.

• B. With 90% confidence, it can be said that the population mean price lies in the first interval. With 95% confidence, it can be said that the population mean price lies in the second interval. The 95% confidence interval is narrower than the 90%.

• C. With 90% confidence, it can be said that the sample mean price lies in the first interval. With 95% confidence, it can be said that the sample mean price lies in the second interval. The 95% confidence interval is wider than the 90.

Which interval is wider? Choose the correct answer below.

• The 95% confidence interval

• The 90% confidence interval

Interpret the results.

• You can be 90% confident that the population mean price of the stock is outside the bounds of the 90% confidence interval, and 95% confident for the 95% interval.

• You can be certain that the closing price of the stock was within the 90% confidence interval for approximately 32 of the 36 days, and was within the 95% confidence interval for approximately 34 of the 36 days.

• You can be 90% confident that the population mean price of the stock is between the bounds of the 90% confidence interval, and 95% confident for the 95% interval.

• You can be certain that the population mean price of the stock is either between the lower bounds of the 90% and 95% confidence intervals or the upper bounds of the 90% and 95% confidence intervals.

You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. From a random sample of 75 dates, the mean record high daily temperature in a certain city has a mean of 86.77°F. Assume the population standard deviation is 14.84°F. The 90% confidence interval is (______, ______). (Round to two decimal places as needed.)

• The 90% confidence interval is (85.00, 88.54).

• The 90% confidence interval is (84.50, 89.04).

• The 90% confidence interval is (85.50, 88.04).

• The 90% confidence interval is (86.00, 87.54).