Question

Consider the following hypothesis test. H0: p = 0.45 Ha: p ≠ 0.45 A sample of 200 provided a sample proportion p = 0.443.

(a) Compute the value of the test statistic.

(b) What is the p-value?

(c) At α = 0.05, what is your conclusion?

(d) What is the rejection rule using the critical value? What is your conclusion?

Answer 1

a)

Test statistics

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

= ( 0.443 - 0.45) / Sqrt ( 0.45 * ( 1 - 0.45) / 200)

= -0.20

b)

For two tailed test,

p-value = 2 * P(Z < z)

= 2 * P(Z < -0.20)

= 2 * 0.4207

= 0.8414

c)

Since p-value > 0.05 level, fail to reject H0

d)

Critical values at 0.05 level = -1.96 , 1.96

Rejection rule = Reject H0 if | z | > 1.96

Since test statistics falls in non-rejection region, fail to reject H0