What is a control chart?

What are the grand mean, the UCL, and the LCL of a control chart for the mean?

Why do you suppose ±3 standard errors are used in control charts and not two or even one standard error? Explain.

A significance test is used to prevent a machine from under filling or overfilling quart bottles. On the basis of a sample, the null hypothesis is rejected and the machine is shut down for inspection. A thorough examination reveals that there is nothing wrong with the filling machine. From a statistical standpoint, was there a type error made? If yes, which type? Explain.

Suppose that you perform a significance test regarding a population mean and that the evidence does not warrant rejection of the null hypothesis. When formulating the conclusion to the test, why is the phrase fail to reject the null hypothesis more accurate than the phrase accept the null hypothesis? Why can the null hypothesis not be proved? Explain.