Question

Using = 0.05, test whether the population proportion of college if college graduates who smoke is not the 0.25 rate for the general population. Assume is a sample of 500, 100 college graduates smoke.

Answer 1

H0: p = 0.25

Ha: p 0.25

Sample proportion = 100 / 500 = 0.20

Test statistics

z = ( - p) / sqrt [ p( 1 - p) / n]

= (0.20 - 0.25) / sqrt [ 0.25 * ( 1 - 0.25) / 500 ]

= -2.58

This is test statistics value.

Critical value at 0.05 level = 1.96

Since test statistics falls in rejection region, Reject H0.

We conclude at 0.05 level that we have sufficient evidence to support the claim.