4. Consider the following hypothesis test

A sample of 80 is used and the population standard deviation is 10. Use. Compute the value of the test statistic Z and specify your conclusion for each of the following sample results

x=22.0

x=27.0

x=23.5

x=28.0

Solution: We want to the two-tailed hypotheses

In order to test the hypotheses, we define as in the previous problem:

and corresponds to the standard deviation, corresponds to the sample size. As before, we reject the null hypothesis if , where corresponds as usual to the cutoff point to the standard normal distribution. Since we want 95% confidence level, we take, and as before get that. With this information we can construct the following table: