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 
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 * (1pcap) * (1/N1 + 1/N2))
z = (0.420.46)/sqrt(0.4419*(10.4419)*(1/700 + 1/850))
z = 1.58
Pvalue Approach
Pvalue = 0.1145
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