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# Statistics

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Question 1:
Find the number of successes x suggested by the given statement.

Among 680 adults selected randomly from among the residents of one town, 27.2% said that they favor stronger gun-control laws.

a. 183
b. 184
c. 186
d. 185

Solve the problem.

In a game, you have a 1/29 probability of winning \$106 and a 28/29 probability of losing \$9 What is your expected value?

a. \$3.66

b. \$12.34

c. -\$5.03

d. -\$8.69

Solve the problem.

The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 99 inches, and a standard deviation of 14 inches. What is the probability that the mean annual precipitation during 49 randomly picked years will be less than 101.8 inches?

a. 0.4192

b. 0.9192

c. 0.0808

d. 0.5808

Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation &#963;. Assume that the population has a normal distribution.

The football coach randomly selected ten players and timed how long each player took to perform a certain drill. The times (in minutes) were:
6 15 5 11 11
5 7 9 15 11
Find a 95 percent confidence interval for the population standard deviation &#963;.

a. (2.6, 6.8)

b. (2.5, 6.2)

c. (0.8, 2.4)

d. (2.6, 6.2)

Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation &#963;. Assume that the population has a normal distribution.

College students' annual earnings: 98% confidence; n = 9, x = \$3211, s = \$897

a. \$545 < &#963; < \$1755

b. \$706 < &#963; < \$1170

c. \$606 < &#963; < \$1718

d. \$566 < &#963; < \$1978

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim.

A nationwide study of American homeowners revealed that 64% have one or more lawn mowers. A lawn equipment manufacturer, located in Omaha, feels the estimate is too low for households in Omaha. Can the value 0.64 be rejected if a survey of 490 homes in Omaha yields 331 with one or more lawn mowers? Use &#940; 0.05.

a. Reject null hypothesis. There is sufficient evidence to support the claim that the proportion with lawn mowers in Omaha is 0.64.

b. Fail to reject null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the proportion with lawn mowers in Omaha is 0.64.

c. Reject null hypothesis. There is sufficient evidence to warrant rejection of the claim that the proportion with lawn mowers in Omaha is 0.64.

d. Fail to reject null hypothesis. There is not sufficient evidence to support the claim that the proportion with lawn mowers in Omaha is 0.64.

Find the indicated probability.

A batch consists of 12 defective coils and 88 good ones. Find the probability of getting two good coils when two coils are randomly selected if the first selection is replaced before the second is made.

a. 0.7733

b. 0.7744

c. 0.176

d. 0.0144

Construct the indicated confidence interval for the difference between population proportions p1 - p2. Assume that the samples are independent and that they have been randomly selected.

In a random sample of 300 women, 50% favored stricter gun control legislation. In a random sample of 200 men, 30% favored stricter gun control legislation. Construct a 98% confidence interval for the difference between the population proportions p1 - p2.

a. 0.088 < p1 - p2 < 0.312

b. 0.099 < p1 - p2 < 0.301

c. 0.115 < p1 - p2 < 0.285

d. 0.111 < p1 - p2 < 0.289