Control Charts, Confidence interval

1. A company makes ball bearings for high quality engine components that demand very close tolerances. The company randomly selects 10 ball bearings every hour. Past experience shows the mean diameter to be .37mm with an average range of .04mm (Average R = .04).
a. Set up the X-bar control chart.
b. Set up an R-bar chart.

A new customer is interested in buying your companies ball bearings. They have three potential uses, each with its own tolerances. They are:
1. Mean = .37mm, tolerance = ± .03mm
2. Mean = .40mm, tolerance = ± .035mm
3. Mean = .38mm, tolerance = ± .02mm
Prepare a memo to the marketing department on how to respond to this potential new customer.

A member of the marketing team suggested that if necessary the process control limits be reduced to + or - 2 standard deviations, so that the control limits are within the tolerance limits set by the prospective buyer. Address this issue in your memo.

Another marketing person has suggested that we increase the sampling to 40 ball bearings every hour, and thus catch process errors faster. How would you address this suggestion?

2. A company is wanting to market a new product to their present customers. They survey 100 potential customers and find that 21 would buy he new product. If you presently have 38,232 customers, determine the actual number of customers that would purchase the new product with a 95% level of confidence.

3. Does rejecting a null hypothesis disprove it? Why or why not?