Quantative Analysis of Data - Significance level, variance, and mean
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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 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.
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 ...
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- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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