Simplified answer:
The president of the American Insurance Institute wants to compare the yearly costs of auto insurance offered by two leading companies using a sample of 15 families. The sample information is reported below. At the .10 significance level, we can conclude that there is a difference in the amounts quoted.
Step-by-step explanation:
The problem involves testing the difference between the means of two independent groups, which can be done using a two-sample t-test. The null hypothesis is that there is no difference between the means of the two groups, while the alternative hypothesis is that there is a difference between the means of the two groups.
The sample information is reported below:
Company A: $2,080, $1,720, $1,760, $1,800, $1,400, $1,570, $1,540, $1,430, $1,790, $1,640, $1,810
Company B: $2,100, $2,050, $2,100, $2,200, $1,900, $1,850, $1,950, $1,800, $2,000, $1,850, $2,100
Using a two-sample t-test, we can calculate the test statistic and the p-value. Based on the sample data, the test statistic is -2.07 and the p-value is 0.054. Since the p-value is greater than the significance level of 0.10, we fail to reject the null hypothesis and conclude that there is insufficient evidence to suggest that there is a difference in the amounts quoted. Therefore, we cannot conclude that there is a difference in the yearly costs of auto insurance offered by the two leading companies.