Question

The research department of an insurance company conducted a survey of the cause of automobile accidents in the last calendar year. A random sample of 200 policies written on single persons revealed that 60 had been in at least one accident. A similar survey of 300 policies written on married persons revealed that 75 had been in at least one accident. At the .05 level of significance, is there a significant difference in the proportion of the population of single and married persons having at least one accident during the period of these surveys?

The hypothesis statements for this problem are:

H₀: π_S – π_M = 0   H₁: π_S – π_M ≠ 0

Answer 1

Given : For single persons : n1=200 , x1=60

For married persons : n2=300 , x2=75

The sample proportions are given by ,

p1=x1/n1=60/200=0.30

p2=x2/n2=75/300=0.25

The pooled estimate is ,

P=(x1+x2)/(n1+n2) = (60+75) / (200+300) = 0.27

Q=1-P = 0.73

1) Hypothesis : H₀: π_S – π_M = 0 VS H₁: π_S – π_M ≠ 0

2) The test statistic under Ho is ,

3) Critical value :

4) Decision : Here ,

Therefore , fail to reject the null hypothesis at 0.05 significance level.

5) Conclusion : Hence , there is not sufficient evidence to conclude that there a significant difference in the proportion of the population of single and married persons having at least one accident during the period of these surveys.