Find the stapling feature for the photocopier in our dept to be not very reliable. The industry standard is that only 2% of items should be stapled incorrectly. In a sample of 120 handouts made for a course, 6 were badly stapled.
(a) At a 0.025 significance level using the critical value approach, test to see if the % error is higher than the industry standard. Clearly state your hypothesis and conclusions.
(b) How many incorrectly stapled handouts would have to be in the sample of 120 for you to change your conclusion in (a)? Round to whole handouts?
(c) If the true % of errors for the copier is 2.5%, calculate the probability of making a type II error for your test in part (a). (5 marks)
(d) There is also a photocopier in the co-op office. In a sample of 100 handouts made using this copier, 6 were badly stapled. Compute a 99% confidence interval for the difference in % errors between the dept's copier and the co-op office copier. Let the dept's copier be population 1.
(e) Test if to see if there is a different between the dept's copier and the co-op copier. Use significance level 0.01 and critical value approach. Clearly state your hypothesis and conclusions. Let the dept's copier be population 1.
Problem 2
Most people that travel to Quebec feels that gas prices there tend to be more than in Ontario. Suppose a random sample of 40 gas stations in Ontario in 2010 had an average price of $1.10/litre and a sample of 35 in Quebec was $1.15. Assume the population standard deviation is 0.08 in Ontario and 0.12 in Quebec. Let Ontario be population 1.
(a) Determine if there is a difference in gas prices between Ontario and Quebec. Use a test significance level of 0.01 and p-value approach. Clearly state hypothesis to be tested and conclusions.
(b) Suppose you were writing an article for the Toronto Star about the difference in mean gas prices and at the end of the article you make this statement: "The poll's margin of error for the difference in mean gas price is X, 18 times out of 20" What is the value of x?