Question

Based on information from Harper’s Index, 78 out of a random sample of 100 American adults claim that they would donate a loved one’s organs after death. However, out of a random sample of 100 adult Americans, only 20 claim that they would donate their own organs after death. Does this information indicate that the proportion of adult Americans who would donate a loved one’s organs is higher?

Answer 1

Sample proportion 1 = 78/100 = 0.78

Sample proportion 2 = 20/100 = 0.20

Pooled proportion = (x1+ x2) / (n1 + n2)

= ( 78 + 20) / (100 + 100)

= 0.49

Test statistics

z = (1 - 2) / sqrt [ ( 1 - ) * ( 1 / n1 + 1/ n2) ]

= ( 0.78 - 0.20 ) / sqrt [ 0.49 * 0.51 * ( 1 / 100 + 1 / 100) ]

= 8.20

This is test statistics value

p-value = P( Z > z)

= P( Z > 8.20)

= 0

At 0.05 significance level, since p-value < 0.05 level, we have sufficient evidence to reject H0.

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