1. A survey conducted last year by my students in Business Studies found out that the average net income for Business graduates is $74,914. One of my current students queried the results and decided to repeat the research by taking a random sample of 112 Business Graduates to determine whether the net income figure is different.
(i) Establish the hypotheses
(ii) Determine the appropriate statistical test and sampling distribution
(iii) Specify type I error or α
(iv) Suppose the 112 Business Graduates who respond produce a sample mean of %78,695 and the standard deviation of net incomes - $14,530. Can the student reject the null hypothesis?
2. In a report prepared by the Economic Research Department of a major bank the Department manager maintains that the average annual family income on Metropolis is $48,432. What do you conclude about the validity of the report if a random sample of 400 families shows and average income of $48,574 with a standard deviation of 2000?
- Specify population parameter of interest
- Establish hypotheses (the null and alternative hypotheses)
- Show if the alternative hypothesis is one or two tails
- Decide which statistical test is appropriate to for the hypothesis testing
- Provide the formula for the test statistics you select in (c)
- Specify type one error
- Use p-value OR Use critical value method to determine the critical values
- Make statistical decision
- Provide managerial conclusion
3. Suppose we would like to determine if the typical amount spent per customer for coffee at a coffee kiosk is more than $20.00. A sample of 49 customers over a three-week period was randomly selected and the average amount spent was $22.60. Assume that the standard deviation is known to be $2.50. Using a 0.02 level of significance, can we conclude the typical amount spent per customer is more than $20.00?