Question

Before the 2012 election, pollsters reported that among 762 men, 49% supported Obama, and among 741 women, 58% supported Obama. Compute the appropriate test statistic to test if there is a difference in women’s and men’s support of Obama. (rounding 4 decimal places in each step)

Answer 1

Solution :

Given that,

n₁ =762

Point estimate = sample proportion = ₁ = 0.49

n₂ = 741

Point estimate = sample proportion = ₂ = 0.58

The value of the pooled proportion is computed as,

= ( n1p1+ n2p2) / ( n₁ + n₂ )

= 0.53

1 - = 0.47

Test statistics

z = (₁ - ₂ ) / *(1-) ( 1/n₁ + 1/n₂ )

= (0.49 + 0.58 ) / ( 0.53 * 0.47) ( 1/762 + 1/741)

= -3.4750