1) A trucking firm suspects that the mean lifetime of a certain tire uses is less than 35,000miles. To check the claim the firm randomly selects and tests 54 of these tires and gets a mean life time of 34,570 with a standard deviation of 1200 miles. At a alpha = 0.05 test the trucking firms claims.
2) A local brewery distributes beer in bottles labeled 12 ounces. A government agency thinks that the brewery is cheating it's customers. The agency selects 20 of these bottles, measure their contents, and obtain a sample mean 11.7 ounces with a standard deviation of 0.7 ounces. Use a 0.01 significance level to test the agency's claim that the brewery is cheating it's customers.
3) A local group claims that the police issue at least 60 speeding tickets a day in their area. To prove their point they randomly selected 2 weeks. Their research yields the number of tickets issued for each day. The data is listed below. At alpha = 0.01, test the group's claims using P-values.
This response provides guidelines on checking claims using alphas, significance levels, and p-values.