## Answers

a)

Below are the null and alternative Hypothesis,

Null Hypothesis, H0: p1 = p2

Alternate Hypothesis, Ha: p1 < p2

b)

0.10 is the significance level

c)

p1cap = X1/N1 = 74/546 = 0.1355

p2cap = X2/N2 = 75/455 = 0.1648

pcap = (X1 + X2)/(N1 + N2) = (74+75)/(546+455) = 0.1489

Test statistic

z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))

z = (0.1355-0.1648)/sqrt(0.1489*(1-0.1489)*(1/546 + 1/455))

z = -1.30

P-value Approach

P-value = 0.0974

d)

As P-value < 0.1, reject the null hypothesis.

e)

yes, we can conclde

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