1. Use a chi squared χ2?-test to test the claim sigma squared equals σ2 = 0.53 at the α = 0.05 significance level using sample statistics s2 = 0.539 and n = 21. Assume the population is normally distributed.
(b) Identify the test statistic.
2. A group says that the mean daily lodging cost for a family traveling in Region 1 is the same as in Region 2. The mean daily lodging cost for 32 families traveling in Region 1 is ?$114 with a population standard deviation of ?$21. The mean daily lodging cost for 32 families traveling in Region 2 is ?$123 with a population standard deviation of ?$16.
At α = 0.10, is there enough evidence to reject the? group's claim?
(b) Find the critical? value(s) and identify the rejection? region(s).
The critical? value(s) is/are _______
?(c) Find the standardized test statistic z.
3. A personnel director in a particular state claims that the mean annual income is the same in one of the? state's counties? (County A) as it is in another county? (County B). In County? A, a random sample of 15 residents has a mean annual income of $42,500 and a standard deviation of $8500. In County? B, a random sample of 99 residents has a mean annual income of $38,000 and a standard deviation of $5600. At α = 0.01?. Assume the population variances are not equal. Assume the samples are random and? independent, and the populations are normally distributed.
(b) Find the critical? value(s) and identify the rejection? region(s). The critical value(s) is/are ______
?(c) Find the standardized test statistic. z=______