Introduction to statistics / mat300 spring 2014 – paired comparisons

Introduction to Statistics / MAT300 SPRING 2014

1. Hypothesis test for the difference of population means: Paired comparisons

The owner of a chain of mini-markets wants to compare the sales performance of two of her stores, Store 1 and Store 2. Though the two stores have been comparable in the past, the owner has made several improvements to Store 1 and wishes to see if the improvements have made Store 1 more popular than Store 2. Sales can vary considerably depending on the day of the week and the season of the year, so she decides to eliminate such effects by making sure to record each store’s sales on the same sample of days.
After choosing a random sample of days, she records the sales (in dollars) for each store on these days, as shown in Table 1.

Table 1

Based on these data, can the owner conclude, at the level of significance, that the mean daily sales of Store 1 exceeds that of Store 2? Answer this question by performing a hypothesis test regarding (which is with a letter “d” subscript), the population mean daily sales difference between the two stores. Assume that this population of differences (Store 1 minus Store 2) is normally distributed.

Perform a one-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.