A sample of five measurements, randomly selected from a

Solution 50E

Step1 of 4:

Let us consider a sample of five measurements, randomly selected from a normally distributed population. Also we have

Here our goal is:

a). We need to test the null hypothesis that the mean of the population is 6 against the alternative hypothesis, = .05.

b). We need to test the null hypothesis that the mean of the population is 6 against the alternative hypothesis, = .05.

c). We need to find the observed significance level for each test.

Step2 of 4:

a).

Let us consider test of the hypothesis:

 against

With  level of significance.

Then,

T-test statistics is given by:

    = -2.0640

Therefore, t = -2.0640.

For one tail t-test, the critical value of ‘t’ is given by:

Degrees of freedom is given by: