Question

A car 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?

Answer 1

Answer with explanation:

Let $\mu$ be the population mean.

Null hypothesis : $H_0:\mu\geq26$

Alternative hypothesis : $H_1:\mu<26$

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: $t=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

$t=\dfrac{25.2-26}{\dfrac{1}{\sqrt{5}}}\approx-1.79$

Critical t-value for t=$t_{n-1, \alpha}=t_{4,0.06}=1.9712$

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.