1.A large electronics company wants to estimate the proportion of all households that own GPS machines. What sample size is required that would give the maximum error of 2.0% for a 95% confidence interval? An unscientific survey had an initial result of 30%.
2. The design tolerance thickness for an automotive part is 55 mm to 65 mm. If the process mean thickness is 61mm with a standard deviation of 2.3 mm, then what percentage of the sheets will be acceptable? (i.e. What percentage will fall within the design tolerances?) Assume that the distribution of these parts is normally distributed. Diagram required.
3. A quality control audit has been devised to check on the sampling procedure when a truckload of potatoes arrives at a packing plant. A random sample of 250 is selected and examined for bruises and other defects. The historical defective rate is 5%. Determine the probability that the shipment will contain 8% or more of the potatoes on the truck that are defective. State assumptions and conditions and if they are met. Draw a diagram.
4. Wildlife biologists inspect 165 deer taken by hunters and find 34 or 20.6 % of them carrying ticks that test positive for Lyme disease.
(a) Calculate the 99 % margin of error and confidence interval for the proportion of deer that may carry such ticks.
(b) How many deer are needed to be inspected if the margin of error were to be cut in half?
(c) Comment on the statistical concerns about this study if it were reported in the news.
5. The president of a bank selected a sample of 1500 loan applications to check if the approval or rejection of an application depends on which one of the two loan officers handles the application.
The information obtained from the sample is summarized in the following two-way table.
Approved Rejected
Joe 750 300 1,050
Bill 250 200 450
1000 500 1,500
Test at the 1% significance level if the approval or rejection of a loan application depends on which loan officer handles the application.
6. The manager of an accounting office is studying the problem of incorrect account numbers being entered into the computer system and wishes to produce a p chart. A subgroup of 200 account numbers is selected from each day's entries and checked to determine the number of incorrect entries. The average proportion of such incorrect entries for the last several months is 0.12.
(a) Calculate the control limits for this process.
(b) After the control limits are calculated and drawn on the control chart and the proportions are plotted for every day what are the signals that indicate that something has gone "wrong' with the process? Give at least two different signals with diagrams.
7. The National Centre for Health Statistics reports that the mean systolic blood pressure for males 35-44 years of age is 128 and a standard deviation of 15. A group of 50 executives selected at random are tested and found to have an average of 132.3. Is there statistical evidence that the executives have a different blood pressure than the population? Use a significance level of 0.05. Solve using a confidence interval approach or a hypothesis test.
8. A local donut shop wishes to test out its donuts against those of the competition which is planning to set up in the community. Each of 50 subjects tastes two unidentified donuts and says which is preferred. Thirty-one or 62% of the subjects prefer the local company donuts to the competition's donuts. Test the claim that a majority (over 50%) of people prefer the local company donuts at the significance level of 0.01. What is your practical conclusion? A full hypotheses test is required.