Question

6) Do attitudes about technological change differ between the young and their elders? The April 2014 Pew Research Center reported that 85 of 144 respondents 18 to 29 years old agreed that technology will lead to a better future, whereas 131 of 297 respondents 65 years old or older agreed. Test whether the proportions agreeing that technology will lead to a better future does not differ between the younger group and the older group. Use a a = 0.01 significance level. (18 points total) Step 1: (4 points) Step 2: (5 points) Step 3: (4 points) Step 4: (2 points) Step 5: (3 points)

Answer 1

1)

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

2)

p1cap = X1/N1 = 85/144 = 0.5903
p1cap = X2/N2 = 131/297 = 0.4411
pcap = (X1 + X2)/(N1 + N2) = (85+131)/(144+297) = 0.4898

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.5903-0.4411)/sqrt(0.4898*(1-0.4898)*(1/144 + 1/297))
z = 2.94

3)

P-value Approach
P-value = 0.0033

4)

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

5)

There is sufficient evidence to conclude that the claim