Question

A sample of 36 observations is selected from a normal population. The sample mean is 49, the population standard deviation is 5. Conducting the following test of hypothesis using the 0.05 significance level, we want to know whether the population mean is no different from 50. Is this a one-tailed test or two tailed test ?

Answer 1

A sample of 36 observations is selected from a normal population. The sample mean is 49 and the population standard deviation is 5.

At 5% level of significance we want to test whether the population mean is no different from 50.

The hypothesis testing problem is:

Since the alternative hypothesis is type, this is a two tailed test.

The test statistic is:

P value for two tail test is:

. ### by using z table

Since p value is greater than 0.05, we are unable to reject the null hypothesis.