Q10

#1 You want to buy a washing machine, and a salesperson tells you that the mean repair costs for Model A and Model B are equal. You research the repair costs. The mean repair cost of

21 Model A washing machines is $208. Assume the population standard deviation is $15. The mean repair cost of 23 Model B washing machines is $230. Assume the population standard deviation is $20. At =0.01, can you reject the salesperson's claim? Assume the samples are random and independent, and the populations are normally distributed. Complete parts (a) through (e).

(a) Identify the claim and state H₀ and H_a.

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

c) Find the standardized test statistic z for 12.

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

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

#2 A real estate agency says that the mean home sales price in City A is the same as in City B. The mean home sales price for 25 homes in City A is $127,401. Assume the population standard deviation is $25,873. The mean home sales price for 25 homes in City B is $112,319.

Assume the population standard deviation is $27,111. At =0.01,is there enough evidence to reject the agency's claim? Complete parts (a) through (d) below.

(a) Identify the claim and state H₀ and H_a.

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

(c) Find the standardized test statistic z.

(d) Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim.

#3 Use the t-distribution table to find the critical value(s) for the indicated alternative hypotheses, level of significance , and sample sizes n₁ and n₂. Assume that the samples are independent, normal, and random. Answer parts (a) and (b).

Ha: 12, =0.10, n₁=14, n₂=13

(a) Find the critical value(s) assuming that the population variances are equal.

(b) Find the critical value(s) assuming that the population variances are not equal.

#4 Test the claim about the difference between two population means 1 and 2

at the level of significance . Assume the samples are random and independent, and the populations are normally distributed.

Claim: 1=2; =0.01. Assume 2/1= 2/2

Sample statistics: x₁=30.5, s₁=3.4, n₁=10

and x₂=32.1, s₂=2.3, n₂=16

(a) Identify the null and alternative hypotheses.

(b) Find the standardized test statistic t.

(c) Find the P-value.

(d) Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim.

#5 A marine biologist claims that the mean length of mature female pink seaperch is different in fall and winter. A sample of 15 mature female pink seaperch collected in fall has a mean length of

113 millimeters and a standard deviation of 12 millimeters. A sample of 8 mature female pink seaperch collected in winter has a mean length of 109 millimeters and a standard deviation of

7 millimeters. At =0.02,can you support the marine biologist's claim? Assume the population variances are equal. Assume the samples are random and independent, and the populations are normally distributed. Complete parts (a) through (e) below.

(a) Identify the claim and state H0 and Ha.

(b) Find the critical value(s) and identify the rejection region(s). (c) Find the standardized test statistic.

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