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 indlviduais 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 52 of 100 individuals prefer Cola 2. Complete parts a through c. (a) Conduct a hypothesis test (preferably using technology) H0​:p=P0​ versus H1​:p=P0​ for p0​=0.41,0.42,0.43,…,0.61,0.62,0.63 at the a =0.05 levol of significance. For which values of P0​ do you not reject the null hypothesis? What do each of the values of P0​ represent? Do not reject the null hypothesis for the values of P0​ between and inclusively, (Type integers or decimals. Do not round.) (b) Construct a 95% confidence interval for the proportion of individuals who profer 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 α=0.01. What would happen to the range of vaives for Po for which the null hypothesis is not rejected? Why does this make sense? Choose the correct answer below. A. The range of values would decrease because the corresponding confidence interval would decrease in size. B. The range of values would increase because the corresponding confidence intarval would decrease in size. c. The range of values would increase because the corresponding confidence interval weuld increase in size D. The range of values would decrease because the corresponding confidence interval would increase in aice.