Question

At a high school debate tournament, half of the teams were asked to wear suits and ties and the rest were asked to wear jeans and t-shirts. The results are given in the table below. Test the hypothesis at the 0.05 level that the proportion of wins is the same for teams wearing suits as for teams wearing jeans.

Win Loss

Suit 22 28

T-shirt 28 22. Find the test statistics for the question above

     

Answer 1

p1cap = X1/N1 = 22/50 = 0.44
p1cap = X2/N2 = 28/50 = 0.56
pcap = (X1 + X2)/(N1 + N2) = (22+28)/(50+50) = 0.5

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 = (0.44-0.56)/sqrt(0.5*(1-0.5)*(1/50 + 1/50))
z = -1.2

P-value Approach
P-value = 0.2301
As P-value >= 0.05, fail to reject null hypothesis.

There is not sufficient evidence to conclude that the proportion of wins is different..

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