Suppose that before the minimum wage law change, the underlying mean number of part-time employees per Burger King Restaurant in New Jersey was 20.3. It was thought that the increase in the New Jersey minimum wage may affect the number of part-time employees in restaurants. We are interested in investigating if the underlying mean number of part-time employees per Burger King Restaurant in New Jersey is the same after the law change as that before the law change. To answer this question, the number of part-time employees working for Burger King after the law change was recorded from the random sample of 129 New Jersey Burger King Restaurants. Summary statistics are displayed below:

(a) Carry out a t-test to investigate if the underlying mean number of part-time employees per Burger King Restaurant in New Jersey is the same after the law change as that before 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 a graphics calculator, PASW (SPSS), Excel or t-tables to determine the P-value.

(b) Does your confidence interval from part (a) contain the true mean number of part-time employees working for Burger King in New Jersey after the law change? Briefly explain.