Question

The numbers of successes and the sample sizes are given for independent simple random samples from two populations. Use the two-proportions z-test to conduct the required hypothesis test. Use the critical-value approach. x1 = 24, n1 = 60, x2 = 12, n2 = 40, two-tailed test, α = 0.05

Answer 1

H0: p1 = p2

Ha: p1 $\neq$ p2

Sample proportion $\hat{p}$ 1 = x1 / n1 = 24/60 = 0.4

Sample proportion $\hat{p}$ 2 = x2 / n2 = 12 / 40 = 0.30

Pooled proportion $\hat{p}$ = (x1 + x2 ) / (n1 + n2)

= (24 + 12) / ( 60 + 40)

= 0.36

Test statistics

z = ($\hat{p}$1 - $\hat{p}$ 2) - 0 / sqrt [ $\hat{p}$ ( 1 - $\hat{p}$ ) * ( 1 / n1 + 1 / n2) ]

= (0.40 - 0.30) / sqrt [ 0.36 * ( 1 - 0.36) * [ 1 / 60 + 1 / 40 ] ]

= 1.02

This is test statistics value.

Critical values at 0.05 level = -1.96 , 1.96

Since test statistics falls in non-rejection region, Do not reject H0.

We conclude at 0.05 level that we fail to support the claim.