4. Below is the amount that a sample of 15 customers spent forlunch ($) at a fast-food restaurant: 7.42 6.29 5.83 6.50 8.34 9.517.10 5.90 4.89 6.50 5.52 7.90 8.30 9.60 6.80 Recall the lunch at afast-food restaurant problem from Assignment 4. Let µ represent thepopulation mean amount spent for lunch ($) at a fast-foodrestaurant. Previously you calculated the mean and standarddeviation of the fifteen sample measurements to be x ? = $7.09 ands = $1.406, respectively. Suppose you want to determine if the truevalue of µ differs from $7.50. Specify the null and alternativehypotheses for this test. Since x ? = $7.09 is less than $7.50, amanger wants to reject the null hypothesis. What are the problemswith using such a decision rule? Compute the value of the teststatistic. Find the approximate p-value of the test or usetechnology to find the exact p-value. Select a value of ?, theprobability of a Type I error. What does ? represent in the wordsof the problem. Give the appropriate conclusion, based on theresults of parts d and e. What conditions must be satisfied for thetest results to be valid? In Assignment 4, you found a 95%confidence interval for µ. Does this interval support yourconclusion in part f?
