# Statistical Problem Assistance: Difference in the Mean

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Professor Brunner had students in his Marketing class rate his performance as Excellent, Good, Fair, or Poor. A graduate student collected the ratings and assured the students that Professor Brunner would not receive them until after the course grades had been submitted. The rating (the treatment) a student gave the professor was matched with his/her course grade, which could range from 0 to 100. the data is as follows:

Excellent Good Fair Poor

94 75 70 68

90 68 73 70

85 77 76 72

80 83 78 65

88 80 74

68 65

65

Is there a difference in the mean scores of the students in each of the four rating categories at a 99% confidence level?

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##### Solution Summary

This solution calculates whether there is a difference in the mean scores of students in different categories at a 99% confidence level.

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Solution. We can set up the following hypotheses.

H0: there is NO difference in the mean scores of the students in each of the four rating categories;

H1: there is a difference in the mean scores of the students in each of the four rating categories.

Use Excel, we can ...

###### 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!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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