Answer:
The t-score is -1.8432
Step-by-step explanation:
We are given the following in the question:
98, 99.6, 97.8, 97.6, 98.7, 98.4, 98.9, 97.1, 99.2, 97.4, 99.1, 96.9, 98.8, 99.9, 96.8, 97, 98.7, 97.6, 98.7, 98.2
Formula:
where
are data points,
is the mean and n is the number of observations.
Sum of squares of differences = 16.152
![s = \sqrt{\dfrac{16.152}{49}} = 0.922](https://tex.z-dn.net/?f=s%20%3D%20%5Csqrt%7B%5Cdfrac%7B16.152%7D%7B49%7D%7D%20%3D%200.922)
Population mean, μ = 98.6
Sample mean,
= 98.22
Sample size, n = 20
Sample standard deviation, s = 0.922
First, we design the null and the alternate hypothesis
Formula:
Putting all the values, we have
![t_{stat} = \displaystyle\frac{98.22 - 98.6}{\frac{0.922}{\sqrt{20}} } = -1.8432](https://tex.z-dn.net/?f=t_%7Bstat%7D%20%3D%20%5Cdisplaystyle%5Cfrac%7B98.22%20-%2098.6%7D%7B%5Cfrac%7B0.922%7D%7B%5Csqrt%7B20%7D%7D%20%7D%20%3D%20-1.8432)
The t-score is -1.8432