
Null Hypothesis
A precision instrument is guaranteed to read accurately to within 2 units. A sample of 4 instrument readings on the same object yielded the measurements 353, 351, 351, and 355. Test the null hypothesis that σ=0.7 against the alternative σ >0.7. Use alpha=0.05.

$\displaystyle H_0:\sigma=.7$ vs. $\displaystyle H_a:\sigma>.7$
the test stat is $\displaystyle {(n1)S^2\over \sigma^2_0} ={\sum_{i=1}^4(X_i\bar X)^2\over .49} $
However it's easier to get the sample variance for {1,1,3,5}.
I did that by subtracting 350 from each.
Hence our test stat is $\displaystyle {(n1)S^2\over \sigma^2_0} ={11\over .49}\approx 22.449 $
The rejection region is based on a $\displaystyle \chi^2$ with 3 degrees of freedom
giving us the interval $\displaystyle (7.815,\infty )$
You should at this level (alpha) reject the null hypothesis and accept the alternative hypothesis.