# Quantative Analysis of Data - Significance level, variance, and mean

Refer to the baseball 2000 data attachment.

a. At the .10 significance level, is ther a difference in the variation of the number of stolen bases among the teams that play their home games on natural grass versus artificial turf?

b. Create a variable that classifies a team's total attendance into three groups: less than 2.0 (million), 2.0 up to 3.0, 3.0 and more. At the .05 significance level, is there a difference in the mean number of games won among the three groups?

c. Using the same attendance variable developed in part (b), is there a difference in the mean team batting average?

d. Using the same attendance variable developed in part (b), is there a difference in the mean salary of the three groups?

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#### Solution Preview

Refer to the baeball 2000 data attachment.

a. At the .10 significance level, is ther a difference in the variation of the number of stolen bases among the teams that play their home games on natural grass versus artificial turf?

I don't know what variable can tell us if it is on natural grass or on artificial turf. Is "League"?

If yes, we can form data on sheet 3. Then use Excel, we get

Anova: Single Factor

SUMMARY

Groups Count Sum Average Variance

Column 1 14 2664 190.2857 2838.681

Column 2 16 3182 198.875 1046.383

ANOVA

Source of Variation SS df MS F P-value F crit

Between Groups 550.8595 1 550.8595 0.293241 0.592434 4.195972

Within Groups 52598.61 28 1878.522

Total 53149.47 29

Since p-value=0.592434>0.10, we fail to reject the null hypothesis. We ...

#### Solution Summary

Quantitative analysis of data is given in the solution. The answer is found by using ANOVA tables to find the variance. Excel is used as the tool for this question.