Question 1:
A significant portion of waiters' and waitresses' incomes is derived from tips. This income must be reported on income tax forms. Government tax auditors assume that the average weekly total of tips is RM100. A recently hired tax account who formerly worked as a waitress believes that this figure underestimates the true total. As a result, she has investigated the weekly tips of a randomly selected group of 25 waiters and waitresses and has found the mean and standard deviation to be RM104 and RM20 respectively.
a) At the 5% significance level, is there evidence to indicate that the average weekly total tips exceed RM100?
b) Would your answer in part (a) change if the population standard deviation were known to be RM22?
c) What is the p-value in part (b)?
Question 2:
A factory produces a component that is used in personal computers. Each component is tested prior to shipment to determine whether or not it is defective. In a random sample of 400 units, 340 were found to be good.
a) If the manufacturer claims that during normal operation hours, the defective rate has never been more than 12%. At the 5% significance level, is there evidence to indicate that the manufacturer's claim is false?
b) What is the probability of you making a Type I error in part (a)?
c) What is the p-value of the test above?
Question 3:
The mean length of a small counterbalance bar is 45 millimetres. The production supervisor is concerned that the adjustment of the machine producing the bars has changed. He asks the engineering department to investigate. The engineering department selects a random sample of 12 bars and measures each. The results are reported below in millimetres.
42 39 42 45 43 40 39 41 40 42 43 42
Is it reasonable to conclude that there has been a change in the mean length of bars? Use 5% significance level.
Question 4
The personnel director of a large insurance company is interested in reducing the turnover rate of data processing clerks in the first year of employment. Past records indicate that 25% of all new employees in this area are no longer employed at the end of the first year. Extensive new training approaches are implemented for a sample of 150 new data processing clerks. At the end of the first year 29 of these 150 new recruits were no longer employed
a) At the 1% significance level, is there evidence to indicate that the proportion of data processing clerks who have gone through the new training and are no longer employed is less than 25%?
b) Compute the p-value for the test.