The authors of the paper “Changes in Quantity, Spending, and Nutritional Characteristics of Adult, Adolescent and Child Urban Corner Store Purchases After an Environmental Intervention” (Preventative Medicine [2015]: 81–85) wondered if increasing the availability of healthy food options would also increase the amount people spend at the corner store. They collected data from a representative sample of 5949 purchases at corner stores in Philadelphia after the stores increased their healthy food options. The sample mean amount spent for this sample of purchases was $2.86 and the sample standard deviation was $5.40.

a. Notice that for this sample, the sample standard deviation is greater than the sample mean. What does this tell you about the distribution of purchase amounts?

b. Before the stores increased the availability of healthy foods, the population mean total amount spent per purchase was thought to be about $2.80. Do the data from this study provide convincing evidence that the population mean amount spent per purchase is greater after the change to increase healthy food options? Carry out a hypothesis test with a significance level of 0.05.