In a survey of 2096 U.S. adults, 1740 think football teams of all levels should require players who suffer a head injury to take a set amount of time off from playing to recover. (Adapted from The Harris Poll)

b. Construct a 95% confidence interval for the population proportion. Interpret the results.

You wish to estimate, with 95% confidence, the population proportion of U.S. adults who have taken or planned to take a winter vacation in a recent year. Your estimate must be accurate within 5% of the population proportion.

b. Find the minimum sample size needed, using a prior study that found that 32% of U.S. adults have taken or planned to take a winter vacation in a recent year. (Source: Rasmussen Reports)

In Exercise 19, would it be unusual for the population proportion to be 38%? Explain.

In Exercises 27–30, find the critical values and for the level of confidence c and sample size n.

c = 0.99, n = 10

Since 1935, the Gallup Organization has conducted public opinion polls in the United States and around the world. The table shows the results of Gallup’s World Affairs Poll of 2021, in which 1021 U.S. adults were polled. The remaining percentages not shown in the results are adults who were not sure.

b. What was the greatest value you obtained for p^?

The data set represents the weights (in pounds) of 10 randomly selected black bears from northeast Pennsylvania. Assume the weights are normally distributed. (Source: Pennsylvania Game Commission)

c. Construct a 99% confidence interval for the population standard deviation. Interpret the results.

Since 1935, the Gallup Organization has conducted public opinion polls in the United States and around the world. The table shows the results of Gallup’s World Affairs Poll of 2021, in which 1021 U.S. adults were polled. The remaining percentages not shown in the results are adults who were not sure.

Use technology to find a 95% confidence interval for the population proportion of adults who

a. view foreign trade as an economic opportunity.

Since 1935, the Gallup Organization has conducted public opinion polls in the United States and around the world. The table shows the results of Gallup’s World Affairs Poll of 2021, in which 1021 U.S. adults were polled. The remaining percentages not shown in the results are adults who were not sure.

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Find the minimum sample size needed to estimate, with 95% confidence, the population proportion of adults who feel that China’s economic power is a critical or an important economic threat to the United States. Your estimate must be accurate within 2% of the population proportion.

In Exercises 27–30, find the critical values and for the level of confidence c and sample size n.

c = 0.90, n = 16

In Exercises 27–30, find the critical values and for the level of confidence c and sample size n.

c = 0.98, n = 25

In Exercises 27–30, find the critical values and for the level of confidence c and sample size n.

c = 0.95, n = 13

Which statistic is the best unbiased estimator for μ?

a. s

b. xbar

c. the median

d. the mode

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

a. 90%

b. 95%

c. 98%

d. 99%

In Exercises 5–8, find the critical value zc necessary to construct a confidence interval at the level of confidence c.

c = 0.80

In Exercises 5–8, find the critical value zc necessary to construct a confidence interval at the level of confidence c.

c = 0.97

Graphical Analysis In Exercises 9–12, use the values on the number line to find the sampling error.

Graphical Analysis In Exercises 9–12, use the values on the number line to find the sampling error.

In Exercises 13–16, find the margin of error for the values of c, σ and n.

c = 0.95, σ = 5.2, n = 30

In Exercises 13–16, find the margin of error for the values of c, σ and n.

c = 0.975, σ = 4.6, n = 100

Matching In Exercises 17–20, match the level of confidence c with the appropriate confidence interval. Assume each confidence interval is constructed for the same sample statistics.

c = 0.88

Matching In Exercises 17–20, match the level of confidence c with the appropriate confidence interval. Assume each confidence interval is constructed for the same sample statistics.

c = 0.98

In Exercises 21–24, construct the indicated confidence interval for the population mean μ.

c = 0.95, xbar = 31.39, σ = 0.80, n = 82.

In Exercises 21–24, construct the indicated confidence interval for the population mean μ.

c = 0.80, xbar = 20.6, σ = 4.7, n = 100.

In Exercises 25–28, use the confidence interval to find the margin of error and the sample mean.

(21.61, 30.15)

In Exercises 25–28, use the confidence interval to find the margin of error and the sample mean.

(3.144, 3.176)

In Exercises 29–32, determine the minimum sample size n needed to estimate for the values of c, σ, and E.

c = 0.90, σ = 6.8, E = 1.

In Exercises 29–32, determine the minimum sample size n needed to estimate for the values of c, σ, and E.

c = 0.95, σ = 2.5, E = 1.

In Exercises 29–32, determine the minimum sample size n needed to estimate for the values of c, σ, and E.

c = 0.80, σ = 4.1, E = 2.

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.