HW Problem 36. (5 pts) Delaney’s Hole in the Wall, a popular restaurant in North Conway, New Hampshire, had been selling an average of 89.3 Black N Tans (a menu item) per week. The owner of the establishment believes this number has fallen in recent years after the addition of several similar items to the menu. To test this theory, she randomly samples 34 weeks of sales records which results in a sample mean number of Black N Tans sold per week of 85.8 with a sample standard deviation of 10.5. At the .01 level of significance, is there enough evidence to conclude that the weekly sales of the Black N Tan been reduced? List and clearly label all eight steps.
HW Problem 37. (5 pts) An obsessive aficionado of a certain brand of raisin brand cereal is suspicious of the brand’s claim that there are at least 350 raisins in each of their 20-ounce boxes. He believes that there are in fact fewer than 350 raisins per box. To test his theory, he randomly samples 40 such boxes obtained at various randomly selected grocery stores. This results in a sample mean number of raisins per box of 344 with a sample standard deviation of 36.9 raisins. At the .10 level of significance, is there enough evidence to conclude there are fewer than 350 raisins in the brand’s 20-ounce box? List and clearly label all eight steps.
HW Problem 38. (5 pts) Ten years ago the average employee age at a local manufacturing firm was 31.7 years. Due to rising employee health care benefit costs, the firm’s human resource manager has been tasked with finding out why these costs are rising. She suspects that it may be due to an aging work force and the associated higher health care costs generally attributed to older employees. To find out if her suspicion has merit, she randomly samples 24 employees which results in a sample mean age of 34.6 years with a sample standard deviation of 4.78 years. According to human resource records, there are exactly 426 employees at the firm. At the .01 level significance, is there enough statistical evidence to support her suspicion that average employee age has increased over the last 10 years? List and clearly label all eight steps.
HW Problem 39. (5 pts) An Ashtabula County farmer who grows zucchinis, among other things, determined in the year 2005 that the average weight of his zucchinis was 8.8 pounds. He now wants to determine if the weight of his zucchinis has changed. He therefor randomly samples 20 zucchinis from this year’s crop which results in a sample mean zucchini weight of 9.1 ounces with a sample standard deviation of 1.5 ounces. At the .05 level of significance, has the average weight of the zucchinis changed? List and clearly label all eight steps.