Question

A medical website states that 40% of U.S. adults are registered organ donors. A researcher believes that the proportion is too high and wants to test to see if it is lower. She selects a random sample of 200 adults and finds that 74 of them are registered organ donors. Perform the hypothesis test at the 0.05 level. Compute the P-value and state a conclusion. Question 21 options: There is not enough evidence to conclude that the proportion of registered organ donors is not less than 40%. There is not enough evidence to conclude that the proportion of registered organ donors is less than 40%. P-value

Answer 1

Pvalue = 0.193

There is not enough evidence to conclude that the proportion of registered organ donors is less than 40%

Explanation:

H0 : p = 0.4

H1 : p < 0.4

Test statistic :

z=pˆ−p/√p(1−p)/n

pˆ = 74 / 200 = 0.37

Z = (0.37 - 0.40) / √(0.40(1 - 0.40) / 200

Z = - 0.03 / √0.0012

Z = - 0.03 / 0.0346410

Z = - 0.866

Test statistic = -0.866

The Pvalue :

P(Z < -0.866) = 0.193

α - level = 0.05

If Pvalue < α ; Reject H0

Since Pvalue > α ; There is not enough evidence to conclude that the proportion of registered organ donors is less than 40%