True False47.When testing population proportions, the z statistic can be used when nπand n(1 - π) are greater than five. True False48.To conduct a test of proportions, the assumptions required for the binomial distribution must be met. True False

49.What value does the null hypothesis make a claim about? 50.Test at the 0.01 level the statement that 55% of those families who plan to purchase a vacation residence in Florida want a condominium. The null hypothesis is π= 0.55 and the alternate is . A random sample of 400 families who planned to buy a vacation residence revealed that 228 families want a condominium. What decision should be made regarding the null hypothesis? 51.What is the level of significance? 52.The mean length of a small counter balance bar is 43 millimeters. There is concern that the adjustments of the machine producing the bars have changed. Test the claim at the 0.02 level that there has been no change in the mean length. The alternate hypothesis is that there has been a change. Twelve bars (n = 12) were selected at random and their lengths recorded. The lengths are (in millimeters) 42, 39, 42, 45, 43, 40, 39, 41, 40, 42, 43 and 42. The mean of the sample is 41.5 and the standard deviation 1.784. Computed t = -2.913. Has there been a statistically significant change in the mean length of the bars? 53.A manufacturer wants to increase the shelf life of a line of cake mixes. Past records indicate that the average shelf life of the mix is 216 days. After a revised mix has been developed, a sample of nine boxes of cake mix gave these shelf lives (in days): 215, 217, 218, 219, 216, 217, 217, 218 and 218. At the 0.025 level, has the shelf life of the cake mix increased?