Test the claim about the difference between two population means and at the level of significance α. Assume the samples are random and independent, and the populations are normally distributed.
Claim: μ1≤μ2, α=0.05, Assume (σ1)^2≠(σ2)^2
Sample statistics:
x̅1=2410, s1=175, n1=13 and x̅2=2305, s2=52, n2=10

Test the claim about the difference between two population means and at the level of significance α. Assume the samples are random and independent, and the populations are normally distributed.

Claim: μ1>μ2, α=0.01, Assume (σ1)^2≠(σ2)^2 

Sample statistics:

x̅1=52, s1=4.8, n1=32 and x̅2=50, s2=1.2, n2=40

Testing a Difference Other Than Zero Sometimes a researcher is interested in testing a difference in means other than zero. In Exercises 27 and 28, you will test the difference between two means using a null hypothesis of Ho: μ1-μ2=k, Ho: μ1-μ2>=k or Ho: μ1-μ2<=k . The standardized test statistic is still

Software Engineer Salaries Is the difference between the mean annual salaries of entry level software engineers in Santa Clara, California, and Greenwich, Connecticut, more than \(4000? To decide, you select a random sample of entry level software engineers from each city. The results of each survey are shown in the figure at the left. Assume the population standard deviations are σ1=\)14,060 and σ2=\$13,050 . At α=0.05, what should you conclude? (Adapted from Salary.com)

Constructing Confidence Intervals for μ1-μ2. You can construct a confidence interval for the difference between two population means μ1-μ2 , as shown below, when both population standard deviations are known, and either both populations are normally distributed or both n1>= 30 and n2>=30 . Also, the samples must be randomly selected and independent.

In Exercises 29 and 30, construct the indicated confidence interval for μ1-μ2 .

Architect Salaries Construct a 99% confidence interval for the difference between the mean annual salaries of entry level architects in Denver, Colorado, and Lincoln, Nebraska, using the data from Exercise 28.

Testing the Difference Between Two Means, (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 t, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed.

Pet Food

A pet association claims that the mean annual costs of food for dogs and cats are the same. The results for samples of the two types of pets are shown at the left. At , α=0.10 can you reject the pet association’s claim? Assume the population variances are equal. (Adapted from American Pet Products Association)

Testing a Difference Other Than Zero Sometimes a researcher is interested in testing a difference in means other than zero. In Exercises 27 and 28, you will test the difference between two means using a null hypothesis of Ho: μ1-μ2=k, Ho: μ1-μ2>=k or Ho: μ1-μ2<=k . The standardized test statistic is still

Architect Salaries Is the difference between the mean annual salaries of entry level architects in Denver, Colorado, and Lincoln, Nebraska, equal to \(9000? To decide, you select a random sample of entry level architects from each city. The results of each survey are shown in the figure. Assume the population standard deviations are σ1=\)6560 and σ2=\$6100 . At α=0.01 what should you conclude? (Adapted from Salary.com)

In Exercises 3–6, determine whether a normal sampling distribution can be used. If it can be used, test the claim about the difference between two population proportions and at the level of significance . Assume the samples are random and independent.

Claim: p1≠p2, α=0.01

Sample statistics: x1=35, n1=70, and x2=36, n2=60