Mathematics: Statistics

Students in a classroom were asked to record the number of units of alcohol they consume on a typical night out. The following summary statistics were generated from a random sample of 50 such students enrolled.
Overall
Sample Size: 50
Sample Mean: 11.6
Sample Standard Deviation: 6.31

You are asked to investigate whether there is evidence that the population mean units of alcohol consumed is equal to 5 using a level of significance of 0.01.

1) What is the appropriate null hypothesis for this study?
H0:

2) What is the appropriate alternative hypothesis for this study?
Ha:

3) What is the value of the test statistic?

4)Using the significance level above, what two values determine the appropriate critical region for this question? What is,
i) the upper bound and ii) the lower bound

5) Is there sufficient evidence at the level of significance given to reject the null hypothesis? Yes or No

1) Ho: Mu = 5
2) Ha: Mu is NOT = 5
3) Test statistic z = (xbar - Mu) / SD = (11.6 - 5) / 6.31 = + 1.05
4) lower bound is z = - 2.575
upper bound is z = + 2.575
The area under the standard normal curve between z = - 2.575 and z = + 2.575 represents the acceptance region or critical region.
5) Since the test statistic (z = 1.05) lies in the critical region, it can be said that there is NO sufficient evidence to reject the Ho.
NO...