Question

A researcher is interested in comparing the level of knowledge of U.S. History possessed by university students in various majors. Random samples of Health Science, Business, Social Science, and Fine Arts majors were selected and each student completed a high school senior level standardized U.S. history exam. The spreadsheet in the "US History Knowledge vs Student Major Dataset B" file on Blackboard for today's date contains data showing the test scores (percent correct) for each student by major. Assume that the test scores for students in each major are Normally distributed.

Confidence interval output from Minitab for this data is provided below

Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev -------+---------+---------+---------+-- Health Science 8 56.63 18.93 (---------*--------) Business 8 48.75 20.10 (---------*--------) Social Science 8 70.25 16.27 (--------*--------) Fine Arts 8 56.50 21.61 (---------*--------) -------+---------+---------+---------+-- 45 60 75 90

Determine whether this data provides evidence that there are any statistically significant differences in the average test scores of students majoring in Health Science, Business, Social Science, and Fine Arts. Your answer should include:

- Mean test scores for students in each major.

- Discussion of the conditions, and why they are satisfied or why they are not satisfied. (Regardless of your answer here, assume the conditions are satisfied.)

- Hypotheses, test statistic, degrees of freedom, and P-value.

- Your conclusion regarding the question of whether there are any significant differences in the U.S. history knowledge levels of students with these four majors.

- Your assessment of the nature of any potential relationship(s) between the average U.S. history test score and student majors.

Answer 1

ANSWER::

standard deviations of all 4 looks equal

hence we use 2-sample t-test with equal variance assumed

For Health Science vs Business

since TS < critical value 2.1448 at 0.05 alpha

hence we fail to reject the null hypothesis

we conclude that there is not significant difference between Health Science and Business

p-value= 2 P( t > |TS|) = 0.4563

similarly

You can do this for other 5 comparisons

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