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    confidence interval and hypothesis test

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    Question 1. The data for question 1 is contained in the file, Course_Scores.xls. This problem concerns course scores (on a scale from 0-100) for a large undergraduate computer-programming course. The class is composed of both underclassmen (freshmen and sophomores) and upperclassmen (juniors and seniors). Also, the students are categorized according to their previous mathematical background from previous courses as 'low' or 'high' mathematical background. The variables in the excel file are:

    - Score: On a scale from 0 - 100
    - UpperCI: 1 for upperclassmen, 0 for underclassmen
    - HighMath: 1 for high mathematical background, 0 otherwise

    For the questions below, assume the data in file Course_Scores.xls represent a random sample for all college students. Answer the following questions:

    a. Find the mean score and 95% confidence interval for all students
    b. Find the mean score and 95% confidence interval for all upperclassmen
    c. Find the mean score and 95% confidence interval for all upperclassmen with high math background
    d. The professor of this course believes he has enough evidence to prove the hypothesis that upperclassmen score at least 5 points better, on average, than underclassmen. Do you agree with this statement? Conduct a test at the ± = .05 level of significance.
    e. If we consider a good grade to be a score of 80 or above, is there enough evidence to reject the null hypothesis that the fraction of good grades is the same from low math backgrounds as those with high math backgrounds? Conduct a test at the ± = .05 level of significance.
    f. Perform a similar test as in part e, but instead of math background, compare upperclassmen to underclassmen

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