A random sample of 321 New Jersey and 77 Pennsylvania fast-food restaurants was selected from those fast-food restaurants in this study.  The restaurants were categorised into two levels according to the number of full-time employees after the law change: 5 or fewer, 6 or more. This information is

(a) State the sampling situation for the difference between the estimated proportion of all New Jersey fast-food restaurants that had 5 or fewer full-time employees after the law change and the estimated proportion of all Pennsylvania fast-food restaurants that had 5 or fewer full-time employees after the law change.

(b)  Carry out a t-test to investigate if there is a difference between the proportion of all New Jersey fast-food restaurants that had 5 or fewer full-time employees after the law change and the proportion of all Pennsylvania fast-food restaurants that had 5 or fewer full-time employees after the law change.  Interpret your results, including the 95% confidence interval.

Notes:

(i) You must follow the step-by-step guide to performing a  t-test.

(ii) It is necessary to use either a graphics calculator, PASW (SPSS), Excel or  t-tables to determine the P-value.

(iii) You can check your calculations by using the Excel spreadsheet on Cecil.  Look under Assignment Resources.