Question

It is claimed that the national average for the price of gasoline in $2.66 per gallon. A sample of 25 gas stations in Hays yielded a sample mean of $2.89, and it is known that national standard deviation is σ=0.48. Compute the test statistic for this test

Answer 1

Answer: 2.396

Explanation:

Given : It is claimed that the national average for the price of gasoline in $2.66 per gallon.

i.e. Population mean :
`\mu= \$\ 2.66 \text{ per gallon}`

Sample size :
`n=25`

Sample mean :
`\overline{x}=\$\ 2.89`

Standard deviation :
`\sigma= 0.48`

We assume that the national average for the price of gasoline is normally distributed.

Since the sample size is small (< 30), then we need to calculate t-test statistic for the test .

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

`=(2.89-2.66)/((0.48)/(√(25)))=2.39583333\approx2.396`

Hence, the test statistic for this test = 2.396