# ANOVA

1. A manufacturer of top-of the line tennis rackets claims that its Smack Me tennis racket will change a player's game. Tennis pro currently serves the ball at an average speed at 115 mph with a standard deviation of 2.5 mph. The speeds are normally distributed. The tennis pro decides to test the company's claim and records the speed of his serve for 15 balls using the Smack Me racket. The data are shown in the following table:

Speed (mph)

117.3 115.9

115.1 115.2

116.0 115.0

116.2 113.0

112.9 120.8

115.4 116.9

113.8 114.4

114.2

2. What is the theory underlying ANOVA?

3. The mean length of a small counterbalance bar is 43 millimeters. The production supervisor is concerned that the adjustments of the m machine producing the bars have changed. He asks the Engineering Department to investigate. Engineering selects a random sample of 12 bars and measure each. The results are reported below in millimeters. 42 39 42 45 43 40 39 41 40 42 43 42

Is it reasonable to conclude that there has been a change in the mean length of the bars? Use the .02 significance level.

4. Why do we say that ANOVA compares samples' means, when we are actually comparing variances?

5. In ANOVA, what does F=1 mean?

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#### Solution Summary

1. A manufacturer of top-of the line tennis rackets claims that its Smack Me tennis racket will change a player's game. Tennis pro currently serves the ball at an average speed at 115 mph with a standard deviation of 2.5 mph. The speeds are normally distributed. The tennis pro decides to test the company's claim and records the speed of his serve for 15 balls using the Smack Me racket. The data are shown in the following table:

Speed (mph)

117.3 115.9

115.1 115.2

116.0 115.0

116.2 113.0

112.9 120.8

115.4 116.9

113.8 114.4

114.2

2. What is the theory underlying ANOVA?

3. The mean length of a small counterbalance bar is 43 millimeters. The production supervisor is concerned that the adjustments of the m machine producing the bars have changed. He asks the Engineering Department to investigate. Engineering selects a random sample of 12 bars and measure each. The results are reported below in millimeters. 42 39 42 45 43 40 39 41 40 42 43 42

Is it reasonable to conclude that there has been a change in the mean length of the bars? Use the .02 significance level.

4. Why do we say that ANOVA compares samples' means, when we are actually comparing variances?

5. In ANOVA, what does F=1 mean?