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=\frac{\overline{x}-\mu}{(\sigma)/(√(n))}`

`t=(25.2-26)/((1)/(√(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.