Acar company claims that its cars achieve an average gas mileage of at least 26 miles per gallon. a random sample of five cars form this company have an average gas mileage of 25.2 miles per gallon and a standard deviation of 1 mile per gallon. at α=0.06, can the company’s claim be supported, assuming this is a normally distributed data set?

Let be the population mean.

Null hypothesis :

Alternative hypothesis :

Since the alternative hypothesis is left tailed, so the test is a left-tailed test.

Sample size : n=5 <30 , so we use t-test.

Test statistic:

Critical t-value for t=

Since, the absolute value of t (1.79) is less than the critical t-value , so we fail to reject the null hypothesis.

Hence, we have sufficient evidence to support the company's claim.

step-by-step explanation: