The research department at the home office of New Hampshire Insurance conducts o
ID: 3233043 • Letter: T
Question
The research department at the home office of New Hampshire Insurance conducts ongoing research on the causes of automobile accidents, the characteristics of the drivers, and so on. A random sample of 400 policies written on single persons revealed 120 had at least one accident in the previous three-year period. Similarly, a sample of 600 policies written on married persons revealed that 150 had been in at least one accident. At the .05 significance level, is there a significant difference in the proportions of single and married persons having an accident during a three-year period? Determine the p-value. Hint: For the calculations, assume the single persons as the first sample.
1. The pooled proportion is . (Round your answer to 2 decimal places.)
2. The decision rule is to reject H0 if z is (Click to select)outsideinside the interval (, ). (Negative values should be indicated by a minus sign. Round your answer to 2 decimal places.)
3. The test statistic is z = . (Round your answer to 2 decimal places.)
4. The p-value is . (Round your answer to 4 decimal places.)
5. What is your decision regarding H0? (Click to select)Do not reject.Reject.
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P1 = P2
Alternative hypothesis: P1 P2
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the proportion from population 1 is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a two-proportion z-test.
Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).
1) p = (p1 * n1 + p2 * n2) / (n1 + n2)
p = 0.27
2) zcritical = 1.96
We will reject the null hypothesis if - 1.96 < z < 1.96
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
SE = 0.02866
3) z = (p1 - p2) / SE
z = 1.745
where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.
Since we have a two-tailed test, the P-value is the probability that the z-score is less than -1.74 or greater than 1.74.
4) Thus, the P-value = 0.081
5) Interpret results. Since the P-value (0.081) is greater than the significance level (0.05), we have to accept the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that two proportions are equal.