7. Sampling Distributions & Confidence Intervals: Mean

In Exercises 5 and 6, use the confidence interval to find the margin of error and the sample mean.

(20.75, 24.10)

In Exercises 5 and 6, use the confidence interval to find the margin of error and the sample mean.

(7.428, 7.562)

Determine the minimum sample size required to be 95% confident that the sample mean waking time is within 10 minutes of the population mean waking time. Use the population standard deviation from Exercise 1.

In Exercises 9–12, find the critical value tc for the level of confidence c and sample size n.

c = 0.98, n = 15

In Exercises 13–16, (a) find the margin of error for the values of c, s, and n, and (b) construct the confidence interval for using the t-distribution. Assume the population is normally distributed.

c = 0.90, s = 25.6, n = 16, xbar = 72.1

In Exercises 13–16, (a) find the margin of error for the values of c, s, and n, and (b) construct the confidence interval for using the t-distribution. Assume the population is normally distributed.

c = 0.98, s = 0.9, n = 12, xbar = 6.8

In Exercises 13–16, (a) find the margin of error for the values of c, s, and n, and (b) construct the confidence interval for using the t-distribution. Assume the population is normally distributed.

c = 0.99, s = 16.5, n = 20, xbar = 25.2

Finding the Margin of Error In Exercises 33 and 34, use the confidence interval to find the estimated margin of error. Then find the sample mean. Book Prices A store manager reports a confidence interval of (244.07, 280.97) when estimating the mean price (in dollars) for the population of textbooks.

In Exercise 35, would it be unusual for the population mean to be over \$1500? Explain.

In Exercise 37, does it seem likely that the population mean could be greater than \$70? Explain.

When all other quantities remain the same, how does the indicated change affect the width of a confidence interval? Explain.

a. Increase in the level of confidence

When all other quantities remain the same, how does the indicated change affect the width of a confidence interval? Explain.

b. Increase in the sample size

When all other quantities remain the same, how does the indicated change affect the width of a confidence interval? Explain.

c. Increase in the population standard deviation

Determining a Minimum Sample Size Determine the minimum sample size required when you want to be 99% confident that the sample mean is within two units of the population mean and σ = 1.4. Assume the population is normally distributed.

Paint Can Volumes A paint manufacturer uses a machine to fill gallon cans with paint (see figure). The manufacturer wants to estimate the mean volume of paint the machine is putting in the cans within 0.5 ounce. Assume the population of volumes is normally distributed.

a. Determine the minimum sample size required to construct a 90% confidence interval for the population mean. Assume the population standard deviation is 0.75 ounce.