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Homework2 - α = 0 05(a State the hypotheses of the one-way...

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STA 3024: Homework 2 (Due Tuesday July 13) Questions 1-2: Suppose the USGA wants to compare the mean distance reached of four different brands of golf balls struck with a driver. A completely randomized design is em- ployed with Iron Byron, the USGA’s robotic golfer, using a driver to hit a random sample of each 10 balls of each brand in a random sequence. The distance is recorded for each hit and is recorded. The table below gives the mean distance for each brand along with its standard deviation. Brand A Brand B Brand C Brand D Number of balls 10 10 10 10 Mean distance 250.8 261.1 270.0 249.3 Standard Deviation 4.74 3.87 4.5 5.2 SSB = 2794 . 4 , SSE = 762 . 3 . 1. Write out an ANOVA table showing (a) degrees of freedom(group, error and total), (b) sums of squares (SSB, SSE and SST), and mean squares (MSB and MSE). (Write in table format) 2. Set up the test to compare the mean distances for the four brands with the one-way ANOVA F test using
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Unformatted text preview: α = 0 . 05 . (a) State the hypotheses of the one-way ANOVA F test. (b) Calculate the value of the test statistic. (c) In the next steps, we will compare this test statistic value to an F distribution. What values of df 1 and df 2 should that F distribution have? (d) Using an F table, identify the value of the test statistic that would correspond to a p-value of 0.05. (e) For our data, is the p-value larger or smaller than 0.05? (f) Make a decision about H , and interpret this decision in terms of what it says about the brands of golf balls. (g) Suppose we reject H in part (f), how many different pairwise comparisons would there be ? (h) The Margin of Error (ME) calculated on the basis of Tukey’s 95% simultaneous confidence level is 5.54, using this find which pairs of the true brand mean distances do not differ significantly? Justify your answer....
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