A13-Two Sample T [Key]

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    Assignment 13Comparing two Population Means in Two Independent Samples 1

    A math instructor compared two methods of teaching algebra, new and existing method. He had two

    groups of students. One group of students was taught by new method; and other was taught by existing

    method. For each selected student, he recorded the algebra exam score.

    Data: myData >> algebra.xlsx

    - For each of the following question, keep 3 decimal places (e.g. 0.123)- Try to use Minitab for all calculations

    Question 1 How much evidence is there to support the new method is more effective than the existing

    method for teaching algebra?

    a. Describe the parameter of interest ()mean exam score of all students taught with the new method

    - mean exam score of all students taught with the existing method

    b. State the null and alternative hypothesizes

    Minitab output for answering the rest of questions

    Two-Sample T-Test and CI: New, Present

    Difference = mu (New) - mu (Present)

    Estimate for difference: 9.92

    95% lower bound for difference: 6.58

    T-Test of difference = 0 (vs >): T-Value = 5.06 P-Value = 0.000 DF = 27

    c. Determine the test statistic: d. Determine the p-value: e. There is (choose one) no / weak / some / strong / extremely strongevidence to support the new

    method is more effective than the existing method for teaching algebra.

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    Assignment 13Comparing two Population Means in Two Independent Samples 2

    Question 2 Suppose the new method is more effective than existing method. We are concerned how

    much increase in average algebra exam score that the method produces compared to the existing

    method.

    Minitab output for answering the rest of questions

    Two-Sample T-Test and CI: New, Present

    Difference = mu (New) - mu (Present)

    Estimate for difference: 9.92 (point estimate)

    95% CI for difference: (5.90, 13.94)T-Test of difference = 0 (vs not =): T-Value = 5.06 P-Value = 0.000 DF = 27

    a. Provide a point estimate for : ______________________b. Provide a 95% confidence interval for : ___________________________c. At 95% confidence level, does the interval indicate there is a significant difference in the average

    algebra exam score between two methods?

    Since the confidence interval for contains all values above

    zero, it indicate that the average exam score of the new method is higher.

    d. Interpret the 95% confidence interval to someone who has no knowledge of statisticsWe are 95% confident that students taught with the new method score higher in the

    exam score than those students taught with existing method by between 5.9 percent and

    13.9 percent on average.

    Or

    We are 95% confident that the average exam score of all students taught with the new

    method is higher than the average exam score of all students taught with the existing

    method by between 5.9 percent and 13.9 percent.

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    Assignment 13Comparing two Population Means in Two Independent Samples 3

    Question 3 Validate the conditions for Two-Sample T method as you performed in Question #1 and #2

    Make sure to submit the graph that you used to validate the conditions.

    [write the answers into a separate document]

    (Do not worry the requirement of random sample)

    8580757065

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    8075706560

    New

    Frequen

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    Present

    Histogram of New, Present

    Since both sample distributions are approximately normal, it is reasonable to assume the

    distribution of exam score of all students taught with new or existing method is normal.