Question

6. (10 pts) A petroleum company was testing a new fuel additive to increase fuel efficiency. The mean fuel effi- ciency for all cars without the additive was known to be 25.0 mpg. A random sample of 27 cars was tested with the new additive, and their mean fuel efficiency was 25.65 mpg with a standard deviation of 1.89 mpg. Test the company’s hypothesis at the 0.05 level of significance.

Answer 1

n = 27

The test hypothesis is

This is a one-sided test because the alternative hypothesis is formulated to detect the difference from the hypothesized mean on the upper side

Now, the value of test static can be found out by following formula:

Since the sample size is n = 27, degrees of freedom on the t-test statistic are n-1 = 27-1 = 26
This implies that

Since , we reject the null hypothesis in favor of the alternative hypothesis