Question

A car company claims that its new SUV gets better gas mileage than its competitor’s SUV. A random sample of 35 its SUV’s has a mean gas mileage of 12.6 miles per gallon (mpg). The population standard deviation is known to be 0.4 mpg. A random sample of 31 competitor’s SUV’s has a mean gas mileage of 12.4 mpg. The population standard deviation for the competitor is known to be 0.3 mpg. Test the company’s claim at the 0.05 level of significance. (round to two decimal places)

A) 6.67
B) 7.39
C) 6.12
D) 7.80

Answer 1

To test the company's claim, we can use a two-sample t-test.

Step-by-step explanation:

To test the company's claim, we can use a two-sample t-test. The null hypothesis (H0) is that the mean gas mileage of the new SUV is not greater than the mean gas mileage of the competitor's SUV. The alternative hypothesis (Ha) is that the mean gas mileage of the new SUV is greater than the mean gas mileage of the competitor's SUV. We can calculate the test statistic using the formula:

t = (sample mean difference - hypothesized mean difference) / (standard error of the difference)

After calculating the test statistic, we can compare it to the critical value from the t-distribution table or calculate the p-value. If the test statistic is greater than the critical value or the p-value is less than the significance level (0.05), we reject the null hypothesis and conclude that there is evidence to support the company's claim.