Question

14.Question Details A marketing consultant was hired to visit a random sample of five sporting goods stores across the state of part of a large franchise of sporting goods stores. The consultant taught the managers of each store better display their goods. The net sales for 1 month before and 1 month after the consultant's visit were consultant's visit were recorded as follows for each thousands of dollars): Store Before After visit 63.3 101.8 57.8 81.2 41.9 visit 57.5 94.849.2 77.4 43.2 that the average net sales improved? Use α-005.(Let d-before-after.) What are we testing in this problem? O single mean paired difference single proportion O difference of proportions difference of means What is the level of significance? State the null and alternate hypotheses. What sampling distribution will you use? What assumptions are you making? The Student's t. We assume that d has an approxdimately uniform distribution. The Student's t. We assume that d has an approximately normal distribution. The standard normal. We assume that d has an approximately noemal distribution. O The standard normal. We assume that d has an approximately uniform distribution. What is the value of the sample test statistic? (Round your answer to three decimal places.) Estimate the P-value. P-value > 0.250 0 0.125 < P-value 0.250 0.050<P-value < 0.125 0.025 < P-value < 0.050 0.005 < P-value < 0.025 p-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value.

Answer 1

Here we have: d -4.78 S 3.824 Correct option "B" Paired difference The level of significance 0.05 Hypothesis: Correct option "D" Hai μ > 0

Correct option "B" The student's t. we assume that d has an approximately normal distribution. Test statistics: t-distribution (σ unknown) t-FM = -4.78-0 tsxT- 3.824-=- 2.795 df n-1-5-1-4 P-value-p (t>l-2.7951) 0.0026 Correct option "D" 0.025<p-value<0.050 Correct option "A"

At the α-0.05 level, we reject the null hypothesis and conclude the data are statistically significant. Correct option "A" There is sufficient evidence at the 0.05 to conclude that the average net sales have improved.