1) Perform the Following Hypothesis Tests (@ = 0.05 in cach case) Data Summary: x = 22; s = 3, n = 36 (1) Ho : 1= 20; H. : A =20 (b) H : 02 =16; H : 02 #2 (c) Explain how you could use part (a) to answer part (b). 3) A survey of 50 U.S. adults and it was found that 5 planned to file their taxes today (April 15). (a) Find a 95% CI for for p (the proportion of US adults filing their their taxes today today.) (b) How large should the sample be if we are going to have a CI of radius less than 0.01 4) Suppose that in a survey of 25 people, it was found that 15 said they liked pancakes. In another survey of 20 people, 10 people said they liked waffles. It seems that maybe the proportion of people that like pancakes is higher than the proportion of people that like waffles. (a) Formulate the relevant hypothesis test. (b) Find the value of the test statistic and the attained level of significance (p-value.) 5) Suppose the were are going to a test / : = 100; /,: / > 100 , with significance level = 0.05. Furthermore, we will be sampling from normally distributed population with o a 10, and taking a sample of sixe n = 25 (a) Find the probability of making a type I error given that / = 99 (b) Find the probability of making a type II error given that & = 105 (c) If we had n = 100, would your probabilities in parts (a) and (b) go up or down