7. Sampling Distributions & Confidence Intervals: Mean

In Exercises 13 and 14, use the confidence interval to find the margin of error and the sample mean.

(14.7, 22.1)

In Exercises 9–12, construct the indicated confidence interval for the population mean μ using the t-distribution. Assume the population is normally distributed.

c = 0.99, xbar = 24.7, s = 4.6, n = 50

In Exercises 9–12, construct the indicated confidence interval for the population mean μ using the t-distribution. Assume the population is normally distributed.

c = 0.98, xbar = 4.3, s = 0.34, n = 14

In Exercises 7 and 8, find the margin of error for the values of c, s, and n.

c = 0.99, s = 3, n = 6

In Exercises 7 and 8, find the margin of error for the values of c, s, and n.

c = 0.95, s = 5, n = 16

Describe how the t-distribution curve changes as the sample size increases.

Finite Population Correction Factor In Exercises 57 and 58, use the information below.

In this section, you studied the construction of a confidence interval to estimate a population mean. In each case, the underlying assumption was that the sample size n was small in comparison to the population size N. When n ≥ 0.05N however, the formula that determines the standard error of the mean needs to be adjusted, as shown below.

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Recall from the Section 5.4 exercises that the expression sqrt[(N-n)/(n-1)] is called a finite population correction factor. The margin of error is

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Use the finite population correction factor to construct each confidence interval for the population mean.

c. c = 0.95, xbar = 40.3, σ = 0.5, N = 300, n = 68.

Finite Population Correction Factor In Exercises 57 and 58, use the information below.

In this section, you studied the construction of a confidence interval to estimate a population mean. In each case, the underlying assumption was that the sample size n was small in comparison to the population size N. When n ≥ 0.05N however, the formula that determines the standard error of the mean needs to be adjusted, as shown below.

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Recall from the Section 5.4 exercises that the expression sqrt[(N-n)/(n-1)] is called a finite population correction factor. The margin of error is

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Use the finite population correction factor to construct each confidence interval for the population mean.

a. c = 0.99, xbar = 8.6, σ = 4.9, N = 200, n = 25.

When all other quantities remain the same, how does the indicated change affect the minimum sample size requirement? Explain.

b. Increase in the error tolerance

When estimating the population mean, why not construct a 99% confidence interval every time?

Soccer Balls A soccer ball manufacturer wants to estimate the mean circumference of soccer balls within 0.15 inch.

a. Determine the minimum sample size required to construct a 99% confidence interval for the population mean. Assume the population standard deviation is 0.5 inch

Juice Dispensing Machine A beverage company uses a machine to fill half-gallon bottles with fruit juice (see figure). The company wants to estimate the mean volume of water the machine is putting in the bottles within 0.25 fluid ounce.

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a. Determine the minimum sample size required to construct a 95% confidence interval for the population mean. Assume the population standard deviation is 1 fluid ounce.

Constructing a Confidence Interval In Exercises 25–28, use the data set to (c) construct a 99% confidence interval for the population mean. Assume the population is normally distributed.

SAT Scores The SAT scores of 12 randomly selected high school seniors

Constructing a Confidence Interval In Exercises 25–28, use the data set to (c) construct a 99% confidence interval for the population mean. Assume the population is normally distributed.

Homework The weekly time spent (in hours) on homework for 18 randomly selected high school students

Constructing a Confidence Interval In Exercises 31 and 32, use the data set to (a) find the sample mean

[APPLET] Earnings The annual earnings (in dollars) of 32 randomly selected intermediate level life insurance underwriters (Adapted from Salary.com)