Blue Crabs A marine researcher claims that the stomachs of blue crabs from one location contain more fish than the stomachs of blue crabs from another location. The stomach contents of a sample of 25 blue crabs from Location A contain a mean of 320 milligrams of fish and a standard deviation of 60 milligrams. The stomach contents of a sample of 15 blue crabs from Location B contain a mean of 280 milligrams of fish and a standard deviation of 80 milligrams. At , α= 0.01can you support the marine researcher’s claim? Assume the population variances are equal.

In Exercises 11–16, test the claim about the difference between two population means μ1 and μ2 at the level of significance α. Assume the samples are random and independent, and the populations are normally distributed.

Claim: μ1> μ2; α=0.10. Assume (σ1)^2 ≠ (σ2)^2

Sample statistics: x̅1= 520, s1= 25, n1= 7 and x̅2= 500, s2= 55, n2= 6

In Exercises 1–5, (a) identify the claim and state H0 and Ha, (b) decide which nonparametric test to use, (c) find the critical value(s), (d) find the test statistic, (e) decide whether to reject or fail to reject the null hypothesis, and (f) interpret the decision in the context of the original claim.

An employment agency claims that there is a difference in the weekly earnings of employees who are union members and employees who are not union members. The table shows the weekly earnings (in dollars) for a random sample of nine union members and eight nonunion members. At , can you support the agency’s claim? (Adapted from U.S. Bureau of Labor Statistics)

In Exercises 11–16, test the claim about the difference between two population means μ1 and μ2 at the level of significance α. Assume the samples are random and independent, and the populations are normally distributed.

Claim: μ1< μ2; α=0.10. Assume (σ1)^2 ≠ (σ2)^2

Sample statistics: x̅1=0.015, s1=0.011, n1= 8 and x̅2=0.019, s2=0.004, n2= 6

A pediatrician claims that the mean birth weight of a single-birth baby is greater than the mean birth weight of a baby that has a twin. The mean birth weight of a random sample of 85 single-birth babies is 3086 grams. Assume the population standard deviation is 563 grams. The mean birth weight of a random sample of 68 babies that have a twin is 2263 grams. Assume the population standard deviation is 624 grams. At α=0.10, can you support the pediatrician’s claim? Interpret the decision in the context of the original claim.

Annual Income

A politician claims that the mean household income in a recent year is greater in York County, South Carolina, than it is in Elmore County, Alabama. In York County, a sample of 23 residents has a mean household income of $64,900 and a standard deviation of $16,000. In Elmore County, a sample of 19 residents has a mean household income of $59,500 and a standard deviation of $23,600. At , α= 0.05can you support the politician’s claim? Assume the population variances are not equal. (Adapted from U.S. Census Bureau)

Independent and Dependent Samples In Exercises 5–8, classify the two samples as independent or dependent and justify your answer.

Sample 1: The IQ scores of 60 females

Sample 2: The IQ scores of 60 males

In Exercises 1–4, classify the two samples as independent or dependent and justify your answer.

Sample 1: The fuel efficiencies of 12 cars

Sample 2: The fuel efficiencies of the same 12 cars using an alternative fuel

In Exercises 1–4, classify the two samples as independent or dependent and justify your answer.

Sample 1: The weights of 45 oranges

Sample 2: The weights of 40 grapefruits