Question

You read an article saying that the average person believes you should wait two years before

marrying a significant other. You want to test the theory that the average college student believes

it should be longer than 2 years. Assume that

σ

= 16

months.

(a.) From the data collected in class, we found that from 77 people who answered the question, the

average number of months people gave was 26.6234. Test your hypothesis at the 5% significance

level.

(b.) If the true average among college students is 30 months, what is the probability you’ll make a

type II error given a sample size of 77?

Answer 1

a) H₀:

    H₁:

The test statistic z = ()/()

                             = (26.6234 - 24)/(16/)

                             = 1.44

P-value = P(Z > 1.44)

             = 1 - P(Z < 1.44)

             = 1 - 0.9251

            = 0.0749

Since the P-value is greater than the significance level(0.0749 > 0.05), so we should not reject the null hypothesis.

At 0.05 significance level, there is not sufficient evidence to conclude that the average college students believes it should be longer than 2 years.

b) At 0.05 significance level, the critical value is z_0.95 = 1.645

z_crit = 1.645

or,( - )/() = 1.645

or, ( - 24)/(16/) = 1.645

or, = 1.645 * 16/ + 24

or, = 26.9994

P(type II error) = = P( < 26.9994)

                                = P(( - )/() < (26.9994 - )/())

                                = P(Z < (26.9994 - 30)/(16/))

                                = P(Z < -1.65)

                                = 0.0495