Question

Consider two independent random samples with the following results: n1=169, x1=125   n2=70, x2=14 Use this data to find the 90% confidence interval for the true difference between the population proportions.

Step 1 of 3: Find the point estimate that should be used in constructing the confidence interval. Round your answer to three decimal places.

Step 2 of 3: Find the margin of error. Round your answer to six decimal places.

Step 3 of 3: Construct the 90% confidence interval. Round your answers to three decimal places.

Answer 1

Here, x1 = 125 , x2 = 14 , n1 = 169 , n2 = 70
p1cap = 125/169 = 0.74 ,
p2cap = 14/70 = 0.2

pcap = (x1 + x2)/(n1 + n2)
pcap = (125 + 14)/(169 + 70)
pcap = 0.5816

Standard Error,
SE = sqrt(pcap * (1-pcap) * (1/n1 + 1/n2))
SE = sqrt(0.5816 * (1-0.5816) * (1/169 + 1/70))
SE = 0.070116

For 90% CI, z-value = 1.64
ME = z*SE = 1.64 * 0.070116 = 0.114990

Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)

CI = (0.74 - 0.2 - 0.114990, 0.74 - 0.2 + 0.114990)

CI = (0.425 , 0.655)