Question

The Business Council of Australia is interested in the level of capitalisation of midcap companies (i.e. companies loosely classified as having a market capitalisation in the mid-range of all companies). They believe that the capitalisation is less than $127 million.

You have been asked to conduct a hypothesis test to determine if the Business Council of Australia is correct. You take a sample of 49 midcap companies and found that the average capitalisation is $123 million with a standard deviation of $11 million.

1. Set up the null and alternative hypotheses words and symbol  

   Ho: (Symbols) and (Words)
   H1:   (Symbols) and (Words)   

2. With a hypothesis test, it is usual to specify a level of significance. Decide on the significance level of alpha (α).
3. On what basis have you chosen the answer to part (b). Could other levels have been appropriate?
4. You have been asked to conduct a hypothesis test to determine if the Business Council of Australia is correct. What condition/assumption must be satisfied before you can do this?
5. Decide on the test statistic to be used. Explain the reasons.
6. Calculate the value of your test statistic.
7. Find the relevant critical value and decide whether H_ois to be rejected or not rejected.
8. Draw an appropriate conclusion.
9. Could your conclusion in part (h) above have been different if α = 10% was used? What about if α = 1% was used? (No calculations required)

Answer 1