Question

In studying his campaign plans, Mr. Singleton wishes to estimate the difference between men and women's views regarding his appeal as a candidate. He asks his campaign manager to take two random independent samples and find the 98% confidence interval for the difference. A random sample of 600male voters and 600female voters was taken. 236 men and 243 women favored Mr. Singleton as a candidate. Find this confidence interval.(8pts)

Step 1.Find the values of the two sample proportions, ?̂1and ?̂2

Step 2.Construct the 98% confidence interval. (Round your answers to 3decimal places.)

Answer 1

1)

p1cap = X1/N1 = 236/600 = 0.3933
p2cap = X2/N2 = 243/600 = 0.4050

2)

Here, , n1 = 600 , n2 = 600
p1cap = 0.3933 , p2cap = 0.405

Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.3933 * (1-0.3933)/600 + 0.405*(1-0.405)/600)
SE = 0.0283

For 0.98 CI, z-value = 2.33
Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.3933 - 0.405 - 2.33*0.0283, 0.3933 - 0.405 + 2.33*0.0283)
CI = (-0.078 , 0.054)