Question

Sleep experts believe that sleep apnea is more likely to occur in men than in the general population. In other words, they claim the percentage of men who suffer from sleep apnea is greater than 5.8%. To test this claim, one sleep expert examines a simple random sample of 90 men and determines 9 of these men suffer from sleep apnea. Does this evidence support the claim that the percentage of men who suffer from sleep apnea not longer equals 5.8%? Use a 0.05 level of significance.

Answer 1

H0: p = 0.058

Ha: p > 0.058

Sample proportion = 9 / 90 = 0.10

Test statistics

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

= 0.10 - 0.058 / sqrt( 0.058 * 0.942 / 90)

= 1.70

This is test statistics value.

Critical value at 0.05 level is 1.645

Since test statistics falls in rejection region, we have sufficient evidence to reject H0.

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