Question

Researchers from the Pew Forum on Religion and Public Life interviewed two random samples of people. Both samples had 1500 people. In 2002, 645 people expressed support for stem-cell research. In 2009, 725 expressed support. If group 1 is the 2002 sample and group 2 is the 2009 sample, run a hypothesis test at the 0.01 level of significance to determine if the proportion of people that support stem cell research has changed since 2002

Answer 1

p1cap = X1/N1 = 645/1500 = 0.43
p1cap = X2/N2 = 725/1500 = 0.4833
pcap = (X1 + X2)/(N1 + N2) = (645+725)/(1500+1500) = 0.4567

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

Rejection Region
This is two tailed test, for α = 0.01
Critical value of z are -2.58 and 2.58.
Hence reject H0 if z < -2.58 or z > 2.58

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.43-0.4833)/sqrt(0.4567*(1-0.4567)*(1/1500 + 1/1500))
z = -2.93

P-value Approach
P-value = 0.0034
As P-value < 0.01, reject the null hypothesis.