Credit Card Debts

1. A credit card watchdog group claims that there is a difference in the mean credit card debts of households in California and Illinois. The results of a random survey of 250 households from each state are shown at the left. The two samples are independent. Assume that s1 = $1045 for California and s2 = $1350 for Illinois. Do the results support the group's claim? Use a = 0.05.

2. A survey indicates that the mean annual wages for forensic science technicians working for local and state governments are $55,950 and $51,100, respectively. The survey includes a randomly selected sample of size 100 from each government branch. Assume that the population standard deviations are $6200 (local) and $5575 (state). The two samples are independent. At a = 0.10, is there enough evidence to conclude that there is a difference in the mean annual wages?

a. Identify the claim and state H0 and Ha.
b. Identify the level of significance a.
c. Find the critical values and identify the rejection regions.
d. Find the standardized test statistic z. Sketch a graph.
e. Decide whether to reject the null hypothesis.
f. Interpret the decision in the context of the original claim.