Suppose you wish to find out the answer to the age-old question, "Do people prefer Cola 1 or Cola 2?" You conduct a blind taste test in which individuals are randomly asked to drink one of the colas first, followed by the other cola, and then asked to disclose which drink they prefer. Results of your taste test indicate that 51 of 100 individuals prefer Cola 2. Complete parts a through c. (a) Conduct a hypothesis test (preferably using technology) Ho: p = Po versus H, : p #Pp for Po = 0.40, 0.41, 0.42, .., 0.60, 0.61, 0.62 at the ox = 0.05 level of significance. For which values of po do you not reject the null hypothesis? What do each of the values of po represent? Do not reject the null hypothesis for the values of po between | |and , inclusively. (Type integers or decimals. Do not round.)(b) Construct a 95% confidence interval for the proportion of individuals who prefer Cola 2 We are 95% confident the proportion of individuals who prefer Cola 2 is between ] and] (Type integers or decimals rounded to three decimal places as needed.) (c) Suppose you changed the level of significance in conducting the hypothesis test to a = 0.01. What would happen to the range of values for po for which the null hypothesis is not rejected? Why does this make sense? Choose the correct answer below. O A. The range of values would increase because the corresponding confidence interval would increase in size O B. The range of values would decrease because the corresponding confidence interval would increase in size. O C. The range of values would increase because the corresponding confidence interval would decrease in size. O D. The range of values would decrease because the corresponding confidence interval would decrease in size