Question

Question 9 An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. Under Age of 18 ni = 500 Number of accidents = 180 SO-3 Over Age of 18 n2 = 600 Number of accidents = 150-36 Soo-.36 ISO - 3 180 360 .64 u 600 We are interested in determining if the accident proportions differ between the two age groups. 2 tauled (a) Write out the null and alternative hypothesis [2] HOLY- - Hailr-1280 (b) Compute the test statistic. [2] 1801150.3 1.36-13-.3 (-:24) So0+6000 = =-59 -2 Jaunat la 04044

Answer 1

a)

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

b)

p1cap = X1/N1 = 180/500 = 0.36
p1cap = X2/N2 = 150/600 = 0.25
pcap = (X1 + X2)/(N1 + N2) = (180+150)/(500+600) = 0.3

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.36-0.25)/sqrt(0.3*(1-0.3)*(1/500 + 1/600))
z = 3.96