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 yield
ed 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
1 answer:
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}](https://tex.z-dn.net/?f=%5Cmu%3D%20%5C%24%5C%202.66%20%5Ctext%7B%20per%20gallon%7D)
Sample size : ![n=25](https://tex.z-dn.net/?f=n%3D25)
Sample mean : ![\overline{x}=\$\ 2.89](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%3D%5C%24%5C%202.89)
Standard deviation : ![\sigma= 0.48](https://tex.z-dn.net/?f=%5Csigma%3D%200.48)
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}}}](https://tex.z-dn.net/?f=t%3D%5Cdfrac%7B%5Coverline%7Bx%7D-%5Cmu%7D%7B%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
![=\dfrac{2.89-2.66}{\dfrac{0.48}{\sqrt{25}}}=2.39583333\approx2.396](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B2.89-2.66%7D%7B%5Cdfrac%7B0.48%7D%7B%5Csqrt%7B25%7D%7D%7D%3D2.39583333%5Capprox2.396)
Hence, the test statistic for this test = 2.396
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