# Statistics

Please read the questions carefully and use Excel to solve the problems. Thank you.

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 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 ...

#### Solution Summary

This is a series of statistics questions that covers contingency tables, analysis of variance, significance level, voting