Question

A theater seats 310 people. Out of the 310 people, 42 of them are dressed up. Use these results with a .05 significance level to test the claim that greater than 15% of people will dress up at the theater.

Answer 1

This is a binomial proportion test. There are only two outcomes either people are dressep up or not.

X:No. of people dressed up in the sample

X = 42 n = 310

Sample = x /n

= 0.1355

We want to test the claim that more than 15% will dress up. Therefore this is one right tailed test

Test

Null: p = 15% (the proportion of people dressed up will be 15%)

Alternative: p > 15% (the proportion of people dressed up will be greater than 15%)

Test Stat :

(null hypothesis) = 15%

Test Stat = -0.7468

p-value = P( Z > |Test stat|)

=P( Z > 0.75)

= 1 - P( Z <0.75)

=1 - 0.77337

p-value = 0.22663

Since p-value > 0.05 (level of significance)

We do not reject the null hypothesis at 5%. There is not sufficient evidence to support that proportion of people dressed up will be greater than 15% at the theatre.

That means the claim fails.