Question

The Big Bang Theory is one of the most popular TV shows. You believe that 50% of all Americans who are 18 to 49 years old have watched the Big Bang Theory last Thursday night. You found a survey result that, of 400 respondents who are between 18 and 49 years old, 221 watched the Big Bang Theory last Thursday.

Then, what is the p-value of your hypothesis?

a.

0.01640

b.

0.03572

c.

0.00694

d.

0.07186

e.

0.10960

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.50

H_a : p 0.50

n = 400

x = 221

= x / n = 221 / 400 = 0.5525

P₀ = 0.50

1 - P₀ = 1 - 0.50 = 0.50

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.5525 - 0.50 / [(0.50 * 0.50) / 400]

= 2.1

Test statistic = 2.1

P(z > 2.1) = 1 - P(z < 2.1) = 1 - 0.9821 = 0.0179

P-value = 2 * 0.0179 = 0.03572

P-value = 0.03572