Question

A researcher claims that 85% of Americans think they are unlikely to contract the Zika virus. In a random sample of 250 Americans, 225 think they are unlikely to contract the Zika virus. With a level of significance of 5%, can you reject the researchers claim?

Answer 1

H0: p = 0.85

Ha: p $\neq$ 0.85

Sample proportion $\hat{p}$ = 225 / 250 = 0.9

Test statistics

z = ($\hat{p}$ - p) / sqrt ( p ( 1 - p) / n)

= ( 0.9 - 0.85) / sqrt ( 0.85 (1 - 0.85) / 250)

= 2.21

Critical values at 0.05 level = -1.96 , 1.96

Since test statistics falls in rejection region, Reject H0.

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