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 : [tex]\mu= \$\ 2.66 \text{ per gallon}[/tex]
Sample size : [tex]n=25[/tex]
Sample mean : [tex]\overline{x}=\$\ 2.89[/tex]
Standard deviation : [tex]\sigma= 0.48[/tex]
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 .
[tex]t=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]=\dfrac{2.89-2.66}{\dfrac{0.48}{\sqrt{25}}}=2.39583333\approx2.396[/tex]
Hence, the test statistic for this test = 2.396
