Question

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Questions 24 - 26

The Big Bang Theory is one of the most popular TV shows. You believe that 50% or more Americans have watched at least an episode of the Big Bang Theory. You found a survey result that, of 100 respondents, 37 have watched at least one episode of the Big Bang Theory. Let p be the population probability of Americans who have watched at least an episode of the Big Bang Theory. You would like to test

H0 :p = 50% H1 :p < 50%

Use these approximations if needed: √ 0.5 × 0.5 = 0.5, √ 0.42 × 0.58 ≈ 0.49, √ 0.37 × 0.63 ≈ 0.48 and √ 0.34 × 0.66 ≈ 0.47.

Q24 What is the p-value of the test?

(a) 5.423%

(b) 10%

(c) 90.318%

(d) 2.091%

(e) 0.466%

Answer (e) 0.466%

Q25 What is the critical value of the test at the signicance level of 10%?

(a) 0.985%

(b) 43.6%

(c) 65.250%

(d) 20.196%

(e) 10%

Answer (b) 43.6%

Q26 Suppose that actually only 42% of Americans have watched at least one episode of the Big Bang Theory. What is the power of the test at the signicance level of 10%? Find the nearest answer.

(a) 86.037%

(b) 38.927%

(c) 62.930%

(d) 19.204%

(e) 10%

Answer (c) 62.930%

Answer 1