Chapter 12: Q4BSC (page 566)
Balanced Design Does the table given in Exercise 1 constitute a balanced design? Why or why not?
Yes, the given experiment is a balanced design as the number of observations under the given two factors is equal.
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Win 4 Lottery Shown below is a histogram of digits selected in California’s Win 4 lottery. Each drawing involves the random selection (with replacement) of four digits between 0 and 9 inclusive.
a. What is fundamentally wrong with the graph?
b. Does the display depict a normal distribution? Why or why not? What should be the shape of the histogram?
c. Identify the frequencies, then test the claim that the digits are selected from a population in which the digits are all equally likely. Is there a problem with the lottery?
In Exercises 1–4, use the following listed arrival delay times (minutes) for American Airline flights from New York to Los Angeles. Negative values correspond to flights that arrived early. Also shown are the SPSS results for analysis of variance. Assume that we plan to use a 0.05 significance level to test the claim that the different flights have the same mean arrival delay time.
Flight 1 | -32 | -25 | -26 | -6 | 5 | -15 | -17 | -36 |
Flight 19 | -5 | -32 | -13 | -9 | -19 | 49 | -30 | -23 |
Flight 21 | -23 | 28 | 103 | -19 | -5 | -46 | 13 | -3 |
Why Not Test Two at a Time? Refer to the sample data given in Exercise 1. If we want to test for equality of the three means, why don’t we use three separate hypothesis tests for\({\mu _1} = {\mu _2},{\mu _1} = {\mu _3}\;and\;{\mu _2} = {\mu _3}\)?
Cola Weights Data Set 26 ‘Cola Weights and Volumes’ in Appendix B lists the weights (lb) of the contents of cans of cola from four different samples: (1) regular Coke, (2) diet Coke, (3) regular Pepsi, and (4) diet Pepsi. The results from the analysis of variance are shown on the top of the next page. What is the null hypothesis for this analysis of variance test? Based on the displayed results, what should you conclude about H0? What do you conclude about the equality of the mean weights of the four samples?
Transformations of Data Example 1 illustrated the use of two-way ANOVA to analyze the sample data in Table 12-3 on page 582. How are the results affected in each of the following cases?
a. The same constant is added to each sample value.
b. Each sample value is multiplied by the same nonzero constant.
c. The format of the table is transposed so that the row and column factors are interchanged.
d. The first sample value in the first cell is changed so that it becomes an outlier.
Speed Dating Data Set 18 “Speed Dating” in Appendix B lists attribute ratings of females by males who participated in speed dating events, and some of those values are included in the table on the top of the next page. Analysis of variance is used with the values in that table, and the StatCrunch results are shown on the next page following the data. Use a 0.05 significance level to test the claim that males in the different age brackets give attribute ratings with the same mean. Does age appear to be a factor in the male attribute ratings?
Age 20-22 | 32 | 34 | 37 | 40.5 | 33 | 28 | 31 | 50 | 39 | 41 |
Age 23-26 | 40 | 21 | 14 | 32 | 26 | 34 | 31 | 34 | 34 | 34 |
Age 27-29 | 31 | 39 | 27 | 34 | 43 | 31 | 30 | 38 | 37 | 34 |
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