Let X equal the thickness of spearmint gum manufactured for vending machines. Assume that the distribution of X is /(J, 0-). The target thickness is 7.5 hundredths of an inch. We shall test the null hypothesis Ho: / = 7.5 against a two-sided alternative hypothesis, using 10 observations. (a) Define the test statistic and critical region for an a =0.05 significance level. Sketch a figure illustrating this critical region. (b) Calculate the value of the test statistic and state your decision clearly, using the following n = 10 thicknesses in hundredths of an inch for pieces of gum that were selected randomly from the production line: 7.65 7.60 7.65 7.70 7.55 7.55 7.40 7.40 7.50 7.50 (c) Is u = 7.50 contained in a 95% confidence interval for u? The mean birth weight of infants in the United States is / = 3315 grams. Let X be the birth weight (in grams) of a randomly selected infant in Jerusalem. Assume that the distribution of X is N(U, o'), where u and of are unknown. We shall test the null hypothesis HO: p = 3315 against the alternative hypothesisH,: