# Statistics

1. Find the indicated critical z value.

Find the value of zα/2 that corresponds to a confidence level of 97.80%.

2. Find the appropriate minimum sample size.

You want to be 95% confident that the sample variance is within 20% of the population variance.

4. Express the confidence interval using the indicated format.

Express the confidence interval 0.457 ± 0.044 in the form of P^ – E < p < P^ + E

4. Use the confidence level and sample data to find the margin of error E. Round your answer to the same number of decimal places as the sample mean unless otherwise noted.

The duration of telephone calls directed by a local telephone company: σ=3.6minutes, n=560, 90%confindence Round your answer to the nearest thousandth.

5. Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test.

A company produces refrigerators for beer kegs. The refrigerators are supposed to maintain a mean temperature of 43°F, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the company and claims that the mean temperature is incorrect. Identify the type II error for the test.

a. Fail to reject the claim that the mean temperature is equal to 43°F when it is actually 43°F.

b. Reject the claim that the mean temperature is equal to 43°F when it is actually different from 43°F.

c. Fail to reject the claim that the mean temperature is equal to 43°F when it is actually different from 43°F.

d. Reject the claim that the mean temperature is equal to 43°F when it is actually 43°F.

6. Find the critical value or values of χ2 based on the given information.

H1: σ > 3.5
n = 14
α = 0.05

7. Find the critical value or values of χ2 based on the given information.

H1: σ ≠ 9.3
n = 28
α = 0.05

8. Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim.

A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation different from the 3.3 mg claimed by the manufacturer. Assuming that a hypothesis test of the claim h
as been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.
a. There is sufficient evidence to support the claim that the standard deviation is different from 3.3 mg

b. There is not sufficient evidence to support the claim that the standard deviation is different from 3.3 mg.

c. There is sufficient evidence to support the claim that the standard deviation is equal to 3.3 mg

d. There is not sufficient evidence to support the claim that the standard deviation is equal to 3.3 mg/

9. Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol for the indicated parameter.

A researcher claims that 62% of voters favor gun control.

a. H0: p < 0.62
H1: p ≥ 0.62

b. H0: p = 0.62
H1: p ≠ 0.62

c. H0: p ≠ 0.62
H1: p = 0.62

d. H0: p ≥ 0.62
H1: p < 0.62

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