Question

Your professor claims that 50% of people in the United States attends church regularly. You think the true percentage is much smaller than this, so you want to investigate. From a random sample of 150 people, you determine that 60 of them attend church regularly. Using alpha = 0.01 ? = 0.01 , determine if your professor is correct.

Answer 1

H0: p = 0.50

Ha: p < 0.50

Sample proportion = 60 / 150 = 0.40

Test statistics

Z = - p / sqrt( p ( 1 - p) / n)

= 0.40 - 0.50 / sqrt( 0.5 * 0.5 / 150)

= -2.45

This is test statistics value.

Critical value at 0.01 level is -2.3263

Since test statistics < -2.3263, we have sufficient evidence to reject H0.

We conclude at 0.01 level that we have enough evidence to support the claim that the true

percentage is much smaller than 50%. (Professor's claim is not correct)