Find Test Value and P-Value

Question

Forty-two percent of people believe that there is life on other planets in the universe. A scientist does not agree with this finding. He surveyed 110 randomly selected individuals and found 44 believed that there is life on other planets. At =α0.05 , is there sufficient evidence to conclude that the percentage differs from 42%? Use the P

-value method with tables.

Answer 1

sample proportion = 44/110 = 0.4

Compute z-statistic = (0.4 - 0.42)/sqrt(0.42*0.58/110) = -0.42

since a 2-sided test, the p-value = 2 * p(z < -0.42) = 2 * 0.3372 = 0.6744

since p-value > 0.05, there is not sufficient evidence that the percentage differs from 0.42.