Question

A peasant satisfaction poll was taken from those living in the North (under the banner of House Stark) and those living in the Stormlands (under the banner of House Baratheon). Of those in the North, 543 were satisfied with their leadership situation and 440 were dissatisfied. Of those in the Stormlands, 461 were satisfied and 532 were dissatisfied. Determine whether the proportion of peasants who are satisfied is higher in the North.

1) State the null and alternative hypotheses.

2) State the value of the test statistic and the p-value.

3) Use a 0.05 significance level to make a decision about the null hypothesis and state your conclusion in context.

Answer 1

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

p1cap = X1/N1 = 543/983 = 0.5524
p1cap = X2/N2 = 461/993 = 0.4642
pcap = (X1 + X2)/(N1 + N2) = (543+461)/(983+993) = 0.5081

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.5524-0.4642)/sqrt(0.5081*(1-0.5081)*(1/983 + 1/993))
z = 3.92

P-value Approach
P-value = 0.0000

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

There is sufficient evidence to concldue that the proportion of peasants who are satisfied is higher in the North.