Test statistic and p-vlaue

Question

Test the claim that the proportion of people who own cats is smaller than 50% at the 0.01 significance level.

The test is:

left-tailed

right-tailed

two-tailed

Correct

Based on a sample of 500 people, 46% owned cats

The test statistic is:  (to 2 decimals)

The p-value is:  (to 2 decimals)

Answer 1

Since alternate hypothesis is less than, then test is left-tailed

test statistic is z = (0.46 - 0.5)/sqrt(0.5*0.5/500) = -1.789 ~ -1.79

since test is left-tailed, p-value is P(z < 1.79) = 0.0367 ~ 0.04