Question

Math 381, Inference Practice 1. For over 50 years, the mean age of registered Democrats in the United States has been 40 years old. A campaign strategist wants to determine if the average age has decreased. A sample of 81 registered Democrats has a mean of 39 years old. The standard deviation is 4 years. Has the mean age decreased significantly? This is a directional, one tail test. a. State the appropriate hypotheses using a=.04. b. Draw the necessary sampling distribution indicating the critical value for a=.04. c. State the p-value. d. State the decision. e. State the conclusion. f. What error is risked?

Answer 1

(a) Ho: M-40 vs Hi u. 40 (b) Here the sampling distribution is it distribution with dt 81-1= 80 - Critical value - - t 80,0 od - 1 (1). - su (x-MHO) 5 ( 39-40) --2:25 P-value = P[ T <-2:25 | Tutso] -0.0136 (d) p-value < x = 0.04 We reject to A at 47 level. (e) Mean age is significantly decreased I at 4% level t it there is actuall no decrease in mean age but decrease in mean age is concluded. So Rejecting to when it true Type - I error risked.