Question

5. We are interested in comparing the proportions of cars that have all-wheel-drive (AWD) between different sizes of cars produced in 2015. In a sample of n = 47 small cars, 9 of these cars had AWD. Also, 9 cars had AWD in a sample of n2 = 34 midsized cars. Conduct a hypothesis test to assess whether there is sufficient evidence of a difference between the proportions of small and midsized cars having AWD. Use a 2-sided alternative hypothesis and a = 0.1.

Answer 1

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

p1cap = X1/N1 = 9/47 = 0.1915
p2cap = X2/N2 = 9/34 = 0.2647
pcap = (X1 + X2)/(N1 + N2) = (9+9)/(47+34) = 0.2222

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.1915-0.2647)/sqrt(0.2222*(1-0.2222)*(1/47 + 1/34))
z = -0.78

P-value Approach
P-value = 0.4342
As P-value >= 0.1, fail to reject null hypothesis.