Question

We are interested in looking at the percentage of households that own dogs in the U.S. and England. We are given the following information:

	Number of people Surveyed	Number of people who own a dog
U.S.	700	294
England	850	391

1. The point estimate for the difference in proportions between people in the U.S. who own dogs and people in England who own dogs is:

2. What is the p-value for this test if we are interested in testing to see if there is simply a difference in the proportions of people who own dogs in the U.S. and England?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 ≠ p2

p1cap = X1/N1 = 294/700 = 0.42
p2cap = X2/N2 = 391/850 = 0.46
pcap = (X1 + X2)/(N1 + N2) = (294+391)/(700+850) = 0.4419

The point estimate for the difference in proportions between people in the U.S. who own dogs and people in England who own dogs is: 0.42 - 0.46 = -0.04

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.42-0.46)/sqrt(0.4419*(1-0.4419)*(1/700 + 1/850))
z = -1.58

P-value Approach
P-value = 0.1145