Consider the following hypothesis test
\( H_0:\mu=18 \)
\( H_a:\mu\ne 18 \)
A sample of 81 provided a sample mean \( \bar{x}=17 \) and a population standard deviation S = 4.5. The value of test statistic and degree of freedom are
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → t = -2 , degree of freedom = 80
The options ask for a t statistic, so the given S = 4.5 is used as the standard deviation from the sample in the one-sample t test:
\( \displaystyle t=\frac{\bar{x}-\mu}{S/\sqrt{n}} \)
\( \displaystyle =\frac{17-18}{4.5/\sqrt{81}} \)
\( \displaystyle =\frac{-1}{0.5} \)
\( \displaystyle =-2 \)
The degrees of freedom are n − 1:
\( \displaystyle 81-1=80 \)