#### Dr. Jayanthi Sankaran

##### Well-Known Member

In the above question #2

A random sample of 36 observations drawn from a normal population returns a sample mean of 18.0 with sample variance of 16.0. Our hypothesis is: the population mean is 15.0 with population variance of 10.0. Which are nearest, respectively, to the test statistic of the sample mean and sample variance (given the hypothesized values, naturally)?

**Answer: (b) t-stat of 4.5 and chi-square stat of 56.0**

I get the above answers easily. For the chi-square test statistic of 56.0 the critical value turns out to be 46.059 at 95% confidence level and so we reject the null hypothesis.

However, we are unable to reject the null hypothesis at 99% confidence because the critical value is 57.342.

All this is okay - my question is, how do we determine the p-value at 35 degrees of freedom and Probabilities of 95% and 99%? Although, the question does not ask this, I am curious to know and learn. Thanks!

Jayanthi