Question

A random sample of 200 voters over the age of 60 were asked whether they thought Social Security benefits should be increased for people over the age of 65. A total of 95 of them answered yes. A random sample of 150 voters aged 18-25 were asked the same question and 63 of them answered yes. Can you conclude that the proportion of voters who support an increase in Social Security benefits is greater among older voters? Use the alpha= 0.05 level. State hypotheses Verify conditions are met Find the value of the test statistic Identify the P-value State decision Conclusion in non-statistical terms

Answer 1

p1cap = X1/N1 = 95/200 = 0.475
p1cap = X2/N2 = 63/150 = 0.42
pcap = (X1 + X2)/(N1 + N2) = (95+63)/(200+150) = 0.4514

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

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.475-0.42)/sqrt(0.4514*(1-0.4514)*(1/200 + 1/150))
z = 1.02

P-value Approach
P-value = 0.1539
As P-value >= 0.05, fail to reject null hypothesis.

There is not sufficient evidence to conclude that the proportion is higher in older group.