Q9

#1 Find the critical value(s) and rejection region(s) for the indicated t-test, level of significance

, and sample size n.

Two-tailed test, =0.01, n=6

#2 Test a claim that the mean amount of lead in the air in U.S. cities is less than 0.037 microgram per cubic meter. It was found that the mean amount of lead in the air for the random sample of

55 U.S. cities is 0.039 microgram per cubic meter and the standard deviation is 0.068

microgram per cubic meter. At =0.10, can the claim be supported? Complete parts (a) through (e) below. Assume the population is normally distributed.

(a) Identify the claim and state H_o and H_a.

(b) Find the critical value(s) and identify the rejection region(s).

(c) Find the standardized test statistic, t.

(d) Decide whether to reject or fail to reject the null hypothesis.

e) Interpret the decision in the context of the original claim.

#3 An employment information service claims the mean annual salary for senior level product engineers is $97,000. The annual salaries (in dollars) for a random sample of 16 senior level product engineers are shown in the table to the right. At =0.10, test the claim that the mean salary is $97,000. Complete parts (a) through (e) below. Assume the population is normally distributed.

(a) Identify the claim and state H_o and H_a.

(b) Find the critical value(s) and identify the rejection region(s).

(c) Find the standardized test statistic, t.

(d) Decide whether to reject or fail to reject the null hypothesis.

e) Interpret the decision in the context of the original claim.

#4 A car company says that the mean gas mileage for its luxury sedan is at least 23 miles per gallon (mpg). You believe the claim is incorrect and find that a random sample of 5 cars has a mean gas mileage of 21 mpg and a standard deviation of 2

mpg. At =0.05, test the company's claim. Assume the population is normally distributed.

(a) State the appropriate hypotheses to test.

(b) What is the value of the standardized test statistic?

(c) What is the critical value?

(d) What is the outcome and the conclusion of this test?

#5 Decide whether the normal sampling distribution can be used. If it can be used, test the claim about the population proportion p at the given level of significance using the given sample statistics.

Claim: p<0.12; =0.10; Sample statistics: p=0.08, n=25

(a) Can the normal sampling distribution be used?

(b) State the null and alternative hypotheses.