Question

A movie website wants to know which movie was the best among the three parts of The Lord of The Rings and surveyed a simple random sample of 40 adults. The results are presented according to 1 = first part, 2 = second part, and 3 =third part.

2 2 3 1 1 3 3 2 3 1 1 3 3 2 2 3 1 3 3 1 2 2 1 3 1 3 3 2 1 1 2 3 2 3 3 1 1 3 2 3'

Let ? = the proportion of adults who prefer the third one.

(1) Find the sample proportion ?̂

(2) Calculate the z-statistic for the test ?0:? ≤ 0.4,??:? > 0.4.

(3) Calculate the p-value

(4) What is the conclusion of the hypothesis test? Use ? = 0.05

do step by step include original formula.

Answer 1

To test the hypothesis of the population proportion values we use the test statistic Z=p-P/sqrt(P*(1-P)/n),n is the sample size and P is the hypothesized value of the proportion. Then Under H₀ Z~N(0,1).The solution with explanations are given in the images...