1. A sporting goods producer claims that the variance of the strengths of a certain fishing line is 15.9. A random sample of 15 spools has a variance of 21.8. At "alpha" = 0.01, can the claim be proven wrong? Assume the population is normally distributed.
2. The standard deviation of the amount of fat in whole milk is claimed to be no greater than 0.50 by the Dairy Association. You do not believe this. You find that a random sample of 31 milk containers has a standard deviation of 0.53. Using "alpha" = 0.05, is there enough evidence to reject the Association's claim? Would your conclusion change if "alpha" = 0.01? Assume the population is normally distributed.
3. A national faculty group conducts salary surveys each year. For 2008, 35 University Professor's had an average salary of $88,200 and 30 Community College Instructor's had an average salary of $73,200. The population standard deviations are known to be $25,800 and $25,600, respectively. At "alpha" = 0.01, can we conclude that university salaries are higher than at the CC's?
4. A USA Today Snapshot states that the government claims that there is a significant difference in the mean credit card debts of households in New York and Texas. A sample of 250 households from each state gave these results: NY mean = $4446.25 with deviation = $845.70 while for TX the mean = $4567.24 with deviation = $561.95. At "alpha" = 0.10, is there a significant difference in debt? Part two: would your conclusion change if "alpha" were .05?