# Math Help - Null Hypothesis

1. ## 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.

2. $H_0:\sigma=.7$ vs. $H_a:\sigma>.7$

the test stat is ${(n-1)S^2\over \sigma^2_0} ={\sum_{i=1}^4(X_i-\bar X)^2\over .49}$

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 ${(n-1)S^2\over \sigma^2_0} ={11\over .49}\approx 22.449$

The rejection region is based on a $\chi^2$ with 3 degrees of freedom
giving us the interval $(7.815,\infty )$

You should at this level (alpha) reject the null hypothesis and accept the alternative hypothesis.