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# Confidence interval of mean

Comparing Two Population Means

Instructor Reputation and Teacher Ratings (revisited)

How powerful are rumors? Frequently, students ask friends and/or look at instructor evaluations to decide if a class is worth taking. Kelley (1950) found that instructor reputation has a profound impact on actual teaching ratings. Towler and Dipboye (1998) replicated and extended this study by asking: Does an instructor's prior reputation affect student ratings?
Subjects were randomly assigned to one of two conditions. Before viewing the lecture, students were given a summary of the instructors' prior teaching evaluations. There were two conditions: Charismatic instructor (frequently at or near the top of the academic department in all teaching categories) and Punitive instructor (frequently near the bottom of the academic department in all important teaching categories). Then all subjects watched the same twenty-minute lecture given by the exact same lecturer. Following the lecture, subjects rated the lecturer. Subjects answered three questions about the leadership qualities of the lecturer. A summary rating score was computed and used as the variable "rating" here.
In these data, condition=1 corresponds to the charismatic teacher and condition=2 correspond to the punitive teacher.

i. Test the difference between the mean ratings of the charismatic-teacher-reputation condition and the punitive-teacher-reputation condition. What is your conclusion based on this test?

ii. Estimate a 95% confidence interval for the mean difference. Do your conclusions differ from part (a)?

2 2.6667
1 1.6667
2 2.0000
1 3.0000
1 1.6667
1 2.3333
2 2.0000
2 1.3333
2 1.6667
1 4.0000
2 2.3333
1 2.3333
2 2.6667
2 2.0000
2 1.6667
1 2.0000
1 2.6667
1 2.6667
1 2.3333
2 1.3333
1 3.3333
2 2.3333
2 2.0000
1 2.3333
2 2.3333
1 2.3333
2 2.3333
2 2.3333
1 2.6667
1 3.0000
1 2.6667
1 3.0000
2 2.3333
1 2.0000
2 1.6667
1 2.3333
2 3.6667
1 2.6667
2 2.3333
1 3.0000
2 2.6667
1 3.3333
1 3.0000
1 2.6667
2 2.0000
2 2.3333
2 2.3333
2 3.3333
1 2.3333.

#### Solution Summary

The solution compares population means using the confidence interval.

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