Statistics
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One hundred people were asked which of four brands of Cola they preferred...
(The material covers Chi-Square Goodness of Fit Tests, Contingency Tables, One-Factor Analysis of Variance, and Two-Factor Analysis.)
(Please use Excel to solve these questions and explain your solution and provide evidence of your work.)
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Solution Summary
This is a series of statistics questions that covers contingency tables, analysis of variance, significance level, voting
Solution Preview
Please see the attached files. The analysis is in the .doc, but some worksheets by Excel are attached as well in the file Q3.xls
(The material covers Chi-Square Goodness of Fit Tests, Contingency Tables, One-Factor Analysis of Variance, and Two-Factor Analysis.)
(Please use Excel to solve these questions and explain your solution and provide evidence of your work.)
Solution. Suppose that the brands are equally popular. Then each brand will have the same percentage 25% of people who preferred. So, we can test
Null hypothesis H0: ;
Alternative hypothesis Ha: is incorrect.
Now we use Chi-squared test. To compute the test statistic, we do the following
3.44
Note that the degree of freedom is df=n-1=4-1=3. For a significance level 0.05, the critical value is 9.488 (See http://planetmath.org/encyclopedia/TableOfCriticalValuesOfChiSquaredDistributions.html ) Since , we fail to reject the null hypothesis H0. At a significance level 0.05, we conclude that the brands are equally popular. In other words, it does not provide sufficient evidence to claim the brands are NOT equally popular.
Solution. To test whether or not female and male students hold different opinion on this question, we need to test and set up two hypotheses:
Null hypothesis H0: The opinions and gender are not related;
Alternative ...
Education
- 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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