Q1) At certain manufacturing plant, machine creates ball bearings which must have a diameter of 0.50 mm. If machine makes ball bearings which are either too small or too large, ball bearings must be scrapped. Every hour, a quality control manager takes random sample of 30 ball bearings to test to see if process is "out of control" (i.e. to test to see if the average diameter differs from 0.50 mm.)

a) Mention the null and alternate hypothesis.   

b) Explain a Type I error for this situation.  

c) Explain a Type II error for this situation.        

Q2) National poll reported that 58% of those with Internet access have made purchase online. To examine whether this percentage applies to its own state, a legislator commissions study. Random sample of 400 state residents who have Internet access is taken. Of those 400 respondents, 215 said that they have made purchases online. Does this sample give enough evidence to conclude that state varies from nation with respect to making purchase online at 0.05 level of significance?