Question

Researchers from the Pew Forum on Religon 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 people 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 increased since 2002.

Answer 1

H0: p1 = p2
Ha: p1 < p2

Here, x1 = 645 , x2 = 725 , n1 = 1500 , n2 = 1500
p1cap = 0.43 , p2cap = 0.4833

pcap = (x1 + x2)/(n1 + n2)
pcap = (645 + 725)/(1500 + 1500)
pcap = 0.4567

Standard Error,
SE = sqrt(pcap * (1-pcap) * (1/n1 + 1/n2))
SE = sqrt(0.4567 * (1-0.4567) * (1/1500 + 1/1500))
SE = 0.0182

Test statistic,
z = (0.43 - 0.4833)/0.0182
z = -2.93

p-value = 0.0017

As p-value < 0.01, reject H0
There are significant evidence to conclude that the proportion of people that support stem cell research has increased since 2002.