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"† wondered if...

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"† 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 5,949 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?

The fact that the sample standard deviation is greater than the sample mean indicates that there is variability in the distribution of purchase amounts. In addition, since purchase amounts cannot be negative, the larger standard deviation indicates that the distribution is .

(b)

Before the stores increased the availability of healthy foods, the population mean total amount spent per purchase was thought to be about $2.81. 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.

State the appropriate null and alternative hypotheses.

H0: μ > 2.81

Ha: μ <>

H0: μ = 2.81

Ha: μ <>

H0: μ = 2.81

Ha: μ > 2.81

H0: μ = 2.81

Ha: μ ≠ 2.81

H0: μ <>

Ha: μ > 2.81
Find the test statistic and P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.)

t

=



P-value

=



State the conclusion in the problem context.

We fail to reject H0. We have convincing evidence that the population mean amount spent per purchase is greater after the change to increased healthy food options.

We reject H0. We do not have convincing evidence that the population mean amount spent per purchase is greater after the change to increased healthy food options.

We fail to reject H0. We do not have convincing evidence that the population mean amount spent per purchase is greater after the change to increased healthy food options.

We reject H0. We have convincing evidence that the population mean amount spent per purchase is greater after the change to increased healthy food options.