Joanna now decides to examine the data for clients who use the Business Advice Only service. She has found that in past studies of businesses of this kind, that the average hours per year spent on Business Advice Only is 21 hours.

Joanna now takes a random sample of 16 clients from the Excel workbook and obtains the following 16 values (client hours per year).

19	21	22	17	16	25	20	23
21	15	21	19	18	21	17	20

a. From the sample data, find the mean (to 2 decimal places) of the time spent obtaining Business Advice Only

Joanna wants to find out whether the hours provided to clients for Business Advice Only are similar to or significantly less than the industry standard which has a population mean of 21 hours. She is interested in this issue because if the average number of hours is less than 21, then it would be useful for the accounting practice to adopt strategies that will raise this average level.

Joanna has obtained the following data to use in her evaluation.

• When testing the hypothesis, she will use the industry standard level of significance of = 5%
• The z-test can be used even though the sample size is only 16 because even though the sample size is < 30 the population data is assumed to have a normal distribution
• She will use a one-tailed z-test
• The critical value of z is -1.645 from the z- table for a one-tailed test
• The population variance for the number of hours spent on business advice only has been found to be 9 hours

b. Based on the commonly used 6-step procedure for hypothesis testing, complete the table below to test whether the mean level of hours provided to clients for Business Advice Only is in fact equal to a population mean of 21 hours or is significantly less than this industry standard.

Step 1	State the null hypothesis and the alternative hypothesis
Step 2	State the level of significance
Step 3	State which test statistic to use
Step 4	State the critical value for the one-tailed test
Step 5	Calculate the value of the test statistic
Step 6	Make a decision to accept or reject the null hypothesis

c. Whilst this question has examined the principles and statistical methods associated with hypothesis testing,you need to be able to explain the decision you reached in step 6 of Question 5b, as though you were explaining it to someone with no statistics background.

d. When Joanna selected a random sample of clients, she had to be sure the sample satisfied the key requirement so the standard procedures used in hypothesis testing could be applied.

What is the key requirement for a sample to be considered a valid sample?

e. Describe 2 different methods of sampling techniques.