A quality control audit has been devised | Complete Solution

1. 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.

2. 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.

3. 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.

4. The following data represents the monthly natural gas consumption (in hundreds of cubic feet) for a family for a random sample of nine months selected from five years of data. The other variable is Degree-days which is a measure of temperature. Degree-days are the number of degrees the average temperature falls below 65 F. SEE ATTACHMENT

(a) Using the Minitab output write the regression model so that you can predict gas consumption knowing the Degree-days. Write the equation in the terms of the actual variables.

(b) Discuss the form, direction and strength of the relationship and verify. Give the correlation coefficient.

(c) Calculate the residual for the first data point in the table. What is the purpose of residual analysis?

State two assumptions necessary for regression analysis