A random sample of 64 observations produced the following

Answer

Step 1 of 2

(a)

We have given a random sample of 64 observations produced the following summary statistics:

We are asked to test the null hypothesis that  against the alternate hypothesis that is  using

 We can write,

Lower tail test about a population mean is,

Figure 1: One Proportion  (lower tail test)

Rejection rule for a lower tail test: The Critical Value Approach from the figure 1

……..(1)

Hence the test statistic for hypothesis tests about a population mean when  is known,

………(2)

We know  hence we can rewrite the equation (2),

………(3)

The rejection region requires   in the lower tail of the

From the table II, Appendix D, the value of

…….(4)

From equation (3) and (4) we can see that the observed value of the test statistic falls in the rejection region.

Since,

Hence  is rejected and there is sufficient evidence to indicate the mean is less than  at