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

Step-by-step 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 .

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

$=\dfrac{2.89-2.66}{\dfrac{0.48}{\sqrt{25}}}=2.39583333\approx2.396$

Hence, the test statistic for this test = 2.396