51. Using a 10% level of significance is there sufficient evidence for Q-Mart to conclude that women charge customers on average spend more than men charge customers? Explain your answer. 52. Using a 1% level of significance is there sufficient evidence for Q-Mart to conclude that women charge customers on average spend more than men charge customers? Explain your answer. 53. The CEO of a software company is committed to expanding the proportion of highly qualified women in the organization’s staff of salespersons. He claims that the proportion of women in similar sales positions across the country in 1999 is less than 45%. Hoping to find support for his claim he directs his assistant to collect a random sample of salespersons employed by his company which is thought to be representative of sales staffs of competing organizations in the industry. The collected random sample of size 50 showed that only 18 were women. Test this CEO’s claim at the .png”>=.05 significance level and report the p-value. Do you find statistical support for his hypothesis that the proportion of women in similar sales positions across the country is less than 40%? QUESTIONS 54 THROUGH 56 ARE BASED ON THE FOLLOWING INFORMATION: Joe owns a sandwich shop near a large university. He wants to know if he is servings approximately the same number of customers as his competition. His closest competitors are Bob and Ted. Joe decides to use a couple of college students to collect some data for him on the number of lunch customers served by each sandwich shop during a weekday. The data for two weeks (10 days) and additional information are shown below (the tables have been generated using StatPro). Summary stats for samples Joe’s Bob’s Ted’s Sample sizes 10 10 10 Sample means 50.700 46.200 43.500 Sample standard deviations 4.244 4.492 3.598 Sample variances 18.011 20.178 12.944 Weights for pooled variance 0.333 0.333 0.333 Number of samples 3 Total sample size 30 Grand mean 46.800 Pooled variance 17.044 Pooled standard deviation 4.128 One-way ANOVA Table Source SS df MS F p-value Between variation 264.60 2 132.30 7.762 0.0022 Within variation 460.20 27 17.044 Total variation 724.80 29 Confidence Intervals for mean difference using 95% confidence level Difference Mean diff Lower Upper Joe’s – Bob’s 4.500 -0.282 9.282 Joe’s – Ted’s 7.200 2.418 11.982 Bob’s – Ted’s 2.700 -2.082 7.482 54. Are all three sandwich shops serving the same number of customers on average for lunch each weekday? Explain how you arrived at your answer. 55. Explain why the weights for the pooled variance are the same for each of the samples. 56. Use the information related to the 95% confidence interval to explain how the number of customers Joe has each weekday compares to his competition. QUESTIONS 57 AND 58 ARE BASED ON THE FOLLOWING INFORMATION: The manager of a consulting firm in Lansing Michigan is trying to assess the effectiveness of computer skills training given to all new entry-level professionals. In an effort to make such an assessment he administers a computer skills test immediately before and after the training program to each of 20 randomly chosen employees. The pre-training and post-training scores of these 20 individuals are shown in the table below. Employee Score before Score after 1 62 77 2 63 77 3 74 83 4 64 88 5 84 80 6 81 80 7 54 83 8 61 88 9 81 80 10 86 88 11 75 93 12 71 78 13 86 82 14 74 84 15 65 86 16 90 89 17 72 81 18 71 90 19 85 86 20 66 92 57. Using a 10% level of significance do the given sample data support that the firm’s training programs is effective in increasing the new employee’s working knowledge of computing? 58. Re-do Question 57 using a 1% level of significance. . QUESTIONS 59 THROUGH 62 ARE BASED ON THE FOLLOWING INFORMATION: Suppose a firm that produces light bulbs wants to know whether it can claim that it light bulbs typically last more than 1500 hours. Hoping to find support for their claim the firm collects a random sample and records the lifetime (in hours) of each bulb. The information related to the hypothesis test is presented below. Test of .png”>.png”>1500 versus one-tailed alternative Hypothesized mean 1500.0 Sample mean 1509.5 Std error of mean 4.854 Degrees of freedom 24 t-test statistic 1.953 p-value 0.031 59. Can the sample size be determined from the information above? Yes or no? If yes what is the sample size in this case? 60. The firm believes that the mean life is actually greater than 1500 hours should you conduct a one-tailed or a two-tailed hypothesis test? Explain your answer.
