Question 2 of 6, Step 2 of 3 $3 / 18$ 3 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 11 people who buy insurance from Company A, the mean cost is $\$ 150$ per month with a standard deviation of $\$ 12$. For 13 randomly selected customers of Company B, you find that they pay a mean of $\$ 159$ per month with a standard deviation of $\$ 18$. Assume that both populations are approximately normal and that the population variances are equal to test Company A's claim at the 0.10 level of significance. Let customers of Company A be Population 1 and let customers of Company B be Population 2. Step 2 of 3 : Compute the value of the test statistic. Round your answer to three decimal places. Answer Tables Keypad Keyboard Shortcuts Submit Answer
Solution
Step 1 ：The question is asking for the value of the test statistic in a hypothesis test comparing the means of two populations. The test statistic in this case is a t-statistic, which is calculated using the formula: \(t = \frac{{mean1 - mean2}}{{\sqrt{{(sd1^2/n1) + (sd2^2/n2)}}}}\) where mean1 and mean2 are the sample means, sd1 and sd2 are the sample standard deviations, and n1 and n2 are the sample sizes.
Step 2 ：In this case, mean1 = 150, mean2 = 159, sd1 = 12, sd2 = 18, n1 = 11, and n2 = 13. We can plug these values into the formula to calculate the t-statistic.
Step 3 ：\(mean1 = 150\)
Step 4 ：\(mean2 = 159\)
Step 5 ：\(sd1 = 12\)
Step 6 ：\(sd2 = 18\)
Step 7 ：\(n1 = 11\)
Step 8 ：\(n2 = 13\)
Step 9 ：Substitute these values into the formula, we get \(t = -1.459724186956822\)
Step 10 ：The value of the test statistic, rounded to three decimal places, is \(\boxed{-1.460}\)
