Question

In a recent survey of drinking laws, a random sample of 1000 women showed that 65% were in favor of increasing the legal drinking age. In a random sample of 1000 men, 60% favored increasing the legal drinking age. Test the claim that the percentage of women favoring a higher legal drinking age is greater than the percentage of men. Use α = 0.05.

a) H0 : _________ H1 : _________ b) Test Statistic: __________ c) Decision: _______________ d) Interpretation/Conclusion:

Answer 1

a)

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

b)

p1cap = X1/N1 = 650/1000 = 0.65
p1cap = X2/N2 = 600/1000 = 0.6
pcap = (X1 + X2)/(N1 + N2) = (650+600)/(1000+1000) = 0.625

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.65-0.6)/sqrt(0.625*(1-0.625)*(1/1000 + 1/1000))
z = 2.31

c)

P-value Approach
P-value = 0.0104
As P-value < 0.05, reject the null hypothesis.

d)

There is sufficient evidence to conclude that the percentage of women favoring a higher legal drinking age is greater than the percentage of men