Chapter 9

9.63 Faced with rising fax costs, a firm issued a guideline that transmissions of ten pages or more should be sent by two-day mail instead. Exceptions are allowed, but they want the average to be ten or below. The firm examined 35 randomly chosen fax transmissions during the next year, yielding a sample mean of 14.44 with a standard deviation of 4.45 pages. (a) At the 0.01 level of significance, is the true mean greater than 10? (b) Use Excel to find the right-tail p value. (LO 3, 4 & 5)

9.66A sample of 100 U.S. one-dollar bills from a Subway cash register revealed that 16 had something written on them besides the normal printing (e.g., "Bob  & Mary"). (a) At α = 0.05, is this sample evidence inconsistent with the hypothesis that 10 percent or fewer of all dollar bills have anything written on them besides the normal printing? Include a sketch of your decision rule and show all calculations. (b) Is your decision sensitive to the choice of α? (c) Find the p value. (LO 3, 4 & 5)

9.87Hammermill Premium Inkjet 24 lb. paper has a specified brightness of 106. (a) At α = 0.005, does this sample of 24 randomly chosen test sheets from a day's production run show that the mean brightness exceeds the specification? (b) Does the sample show that σ² < 0.0025? State the hypotheses and critical value for the left-tailed test from Appendix E. (LO 4 & 6) 

Brightness

Chapter 10

10.39 Do a larger proportion of university students than young children eat cereal? Researchers surveyed both age groups to find the answer. The results are shown in the table below. (a) State the hypotheses used to answer the question. (b) Using α = 0.05, state the decision rule and sketch it. (c) Find the sample proportions and z statistic. (d) Make a decision. (e) Find the p value and interpret it. (f) Is the normality assumption fulfilled? Explain. (LO 2)

10.51 To test the hypothesis that students who finish an exam first get better grades, Prof. Hardtack kept track of the order in which papers were handed in. The first 25 papers showed a mean score of 77.1 with a standard deviation of 19.6, while the last 24 papers handed in showed a mean score of 69.3 with a standard deviation of 24.9. Is there sufficient evidence to support Prof. Hardtack's hypothesis, at α = 0.05? (a) State the hypotheses for a right-tailed test. (b) Obtain a test statistic and p value assuming equal variances. Interpret these results. (c) Is the difference in mean scores large enough to be important? (d) Is it reasonable to assume equal variances? (e) Carry out a formal test for equal variances at α = 0.05, showing all steps clearly. (LO 2)

Chapter 11

Instructions: For each data set: (a) State the hypotheses. (b) Use Excel's Data > Data Analysis (or MegaStat or MINITAB) to perform the one-factor ANOVA, using α = 0.05. (c) State your conclusion about the population means. Was the decision close? (d) Interpret the p value carefully. (e) Include a plot of the data for each group if you are using MegaStat, and confidence intervals for the group means if you are using MINITAB. What do the plots show?

11.1 Scrap rates per thousand (parts whose defects cannot be reworked) are compared for five randomly selected days at three plants. Does the data prove a significant difference in mean scrap rates? (LO 3)  

Instructions: For each data set: (a) State the hypotheses. If you are viewing this data set as a randomized block, which is the blocking factor and why? (b) Use Excel's Data > Data Analysis (or MegaStat or MINITAB) to perform the two-factor ANOVA without replication, using α = 0.05. (c) State your conclusions about the treatment means. (d) Interpret the pvalues carefully. (e) Include a plot of the data for each group if you are using MegaStat, or individual value plots if you are using MINITAB. What do the plots show?

11.6 Concerned about Friday absenteeism, management examined absenteeism rates for the last three Fridays in four assembly plants. Does this sample allow us to conclude that there is a difference in average absenteeism for different plants? (LO 3)  

Chapter 12

12.3 Teenagers make up a large percentage of the market for clothing. Below are data on running shoe ownership in four world regions (excluding China). Research question: At α = 0.01, does this sample show that running shoe ownership depends on world region? (See J. Paul Peter and Jerry C. Olson, Consumer Behavior and Marketing Strategy, 9th ed. [McGraw-Hill, 2004], p. 64.) (LO 1 & 2)  

Running Shoe Ownership in World Regions

12.7 In previous years, exams in a particular statistics course were set by the professor such that 15 percent of students received a grade of A, 25 percent received a grade of B, 30 percent received a grade of C, 20 percent received a grade of D, and 10 percent received a grade of F. This year, the professor decided to change the types of exams he set and the results for a class of 250 students showed that 30 received a grade of A, 55 received a grade of B, 83 received a grade of C, 55 received a grade of D, and 27 received a grade of F. Assuming that these 250 students represent a random sample of students who would be taking this course, is there sufficient evidence, at the 0.05 level of significance, that this new type of exam has affected the grade distribution in this course? (LO 1 & 3)