HW 7.3

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

, and sample size n.

Left-tailed test, =0.025, n=12

(Round to the nearest thousandth as needed.)

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

, and sample size n.

Right-tailed test, =0.05, n=12

(Round to the nearest thousandth as needed.)

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

, and sample size n.

Two-tailed test, =0.02, n=7

(Round to the nearest thousandth as needed.)

#4 Use technology and a t-test to test the claim about the population mean at the given level of significance using the given sample statistics. Assume the population is normally distributed. Claim: >78; =0.10 Sample statistics: x=78.7, s=3.5, n=24

(a) What are the null and alternative hypotheses?

(b) What is the value of the standardized test statistic? (Round to two decimal places as needed.)

(c) What is the P-value of the test statistic?

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

#5 Use a t-test to test the claim about the population mean at the given level of significance

using the given sample statistics. Assume the population is normally distributed. Claim: 25;

=0.01 Sample statistics: x=29.9, s=4.2, n=10

(a) What are the null and alternative hypotheses?

(b) What is the value of the standardized test statistic? (Round to two decimal places as needed.)

(c) What is the P-value of the test statistic?

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

#6 A used car dealer says that the mean price of a three-year-old sports utility vehicle i $24,000. You suspect this claim is incorrect and find that a random sample of 23 similar vehicles has a mean price of $24,582 and a standard deviation of $1906. Is there enough evidence to reject the claim at =0.01?

Complete parts (a) through (e) below. Assume the population is normally distributed.

(a) Write the claim mathematically and identify 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.

#7 An employment information service claims the mean annual salary for senior level product engineers is $96,000. The annual salaries (in dollars) for a random sample of 16 senior level product engineers are shown in the table to the right. At =0.01, test the claim that the mean salary is $96,000.

Complete parts (a) through (e) below. Assume the population is normally distributed.

Annual Salaries

100,611 96,358 93,521 112,826 82,519 74,164 77,055 80,942 102,484 76,184 103,928 104,069 91,118 82,164 85,043 110,306

(a) Write the claim mathematically and identify 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.

#8 A consumer group claims that the mean minimum time it takes for a sedan to travel a quarter mile is greater than 14.8 seconds. A random sample of 23 sedans has a mean minimum time to travel a quarter mile of 15.3 seconds and a standard deviation of 2.09 seconds. At =0.10

is there enough evidence to support the consumer group's claim? Complete parts (a) through (d) below. Assume the population is normally distributed.

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

(b) Find the standardized test statistic, t. Find the P-value.

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

(d) Interpret the decision in the context of the original claim.

#9 You receive a brochure from a large university. The brochure indicates that the mean class size for full-time faculty is fewer than 32 students. You want to test this claim. You randomly select 18 classes taught by full-time faculty and determine the class size of each. The results are shown in the table below. At =0.01, can you support the university's claim? Complete parts (a) through (d) below. Assume the population is normally distributed

(a) Write the claim mathematically and identify H_o and H_a.

(b) Use technology to find the P-value.

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

(d) Interpret the decision in the context of the original cl

#10 A car company says that the mean gas mileage for its luxury sedan is at least 21 miles per gallon (mpg). You believe the claim is incorrect and find that a random sample of 7 cars has a mean gas mileage of 20 mpg and a standard deviation of 5 mpg. At =0.10, test the company's claim. Assume the population is normally distributed.

What is the value of the standardized test statistic?