Question

insurance company a claims that its customers pay less for car insurance, on average, than customers of its competitor, company b. you wonder if this is true, so you decide to compare the average monthly costs of similar insurance policies from the two companies. for a random sample of 12 people who buy insurance from company a, the mean cost is $151 per month with a standard deviation of $14. for 9 randomly selected customers of company b, you find that they pay a mean of $159 per month with a standard deviation of $12. assume that both populations are approximately normal and that the population variances are equal to test company as claim at the 0.05 level of significance. let customers of company a be population 1 and let customers of company b be population 2. step 3 of 3: draw a conclusion and interpret the decision. answer we fail to reject the null hypothesis and conclude that there is sufficient evidence at a 0.05 level of significance to support the claim that customers of company a pay less for car insurance, on average, than customers of company b. we fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.05 level of significance to support the claim that customers of company a pay less for car insurance, on average, than customers of company b. we reject the null hypothesis and conclude that there is insufficient evidence at a 0.05 level of significance to support the claim that customers of company a pay less for car insurance, on average, than customers of company b. we reject the null hypothesis and conclude that there is sufficient evidence at a 0.05 level of significance to support the claim that customers of company a pay less for car insurance, on average, than customers of company b.

Explanation:

Step1: Recall hypothesis - testing decision - rule

If the p - value is greater than the level of significance ($\alpha$), we fail to reject the null hypothesis. If the p - value is less than $\alpha$, we reject the null hypothesis. Here, $\alpha = 0.05$.

Step2: Analyze the claim

The null hypothesis $H_0:\mu_1\geq\mu_2$ and the alternative hypothesis $H_1:\mu_1 < \mu_2$ (Company A's claim). When we fail to reject $H_0$, it means there is not enough evidence to support the claim that $\mu_1 < \mu_2$. When we reject $H_0$, there is enough evidence to support the claim that $\mu_1 < \mu_2$.

Step3: Determine the conclusion

If we fail to reject the null hypothesis, we conclude that there is insufficient evidence at the 0.05 level of significance to support the claim that customers of Company A pay less for car insurance, on average, than customers of Company B.

Answer:

We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.05 level of significance to support the claim that customers of Company A pay less for car insurance, on average, than customers of Company B.