Solution verification for hypothesis testing and confidence interval problem
There's a random sample of size observations over a normally distributed population with standard deviation :
8.7, 7, 4, 7.6, 3, 8.1, 6.4, 6.1, 9.4, 6.2
- Find 96% confidence interval for the population mean
- Test the hypothesis against Ha: with significance level . Find approximation of the observed p value.
We are looking for real numbers l and u s.t.:
We are looking for which from the z-score table is: 2.055. Therefore:
For the second part:
We set two z-scores: from which we construct a two-tailed test.
Our test statistic is: from where we see the test statistic t is not in the rejection region, therefore we fail to reject the null hypothesis.