Evaluating Introductory Statistics Knowledge: A Pre-Test/Post-Test Analysis

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Evaluating Introductory Statistics Knowledge: A Pre-Test/Post-TestAnalysisAt theUniversity of Mytholopoloisthe head of the statistics department wants to findout whether or not 7 basic topics are being adequately learned in introductory statisticscourses.A test is written that has 7 questions, one question addressing each of the maintopics under consideration.These topics are:1-measurement scales2-measures of central tendency3-standard deviation4-normal curve and empirical rule5-t-tests6-ANOVA7-correlation and regressionThis brief test is going to be administered to all students registered in theintroductory statistics course at the beginning of the first session and the end of the lastsession.This is a pre-test/post-test design.But before this full scale data collection effortbegins the department is going to test this little instrument.Eight students are selected touse as a test group.The following is a table of the student scores in the pre-test conditionand the post-test condition.This final project is asking you to consider 4 different statistical tests.The first iswhat the department head is looking for, the second is an extension of that with a furtherbreakdown of information, the third is looking for a relationship between two differentvariables and the fourth is asking what test you would use to predict a students score.StudentSexPre-testPost-testHours perweekstudyingstatisticsMatildaF4615FranklinM2518LilyF4713

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PaulM3611LouiseF557GoldaF4612DuncanM2514PhilipM679Answer the followingquestions about this problem.Preliminary information about the dataQuestion1.What is the head of the statistics department trying to find out?2.What are the variables of interest?3.What is the measurement scale of the each of thevariables of interest?4.What is the mean of the pre-test scores?5.What is the median of the post-test scores?6.In both the pre and post test conditions, considering these as a singlesample, what is the mode?(There should be 16 values considered.)7.What is the range of the hours studied values?8.Can you calculate a mean for the sex of the students involved in this pilotstudy?Explain your answer.9.What is the standard deviation of the pre-test scores?Please show allyourwork. You don't have to do the standard deviation of the post-test scores.10. Looking at just the pre-test scores, using the empirical rule, is thedistribution of these scores normal?11. State the percentages of the empirical rule, before you continue with thenext 3 questions.12. How many of the values fall within 1 SD of the mean?13. How many of these values fall within 1 and 2 SD of the mean?14. How many of these values fall with 2 and 3 SD of the mean?Answer:

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1. The head of thestatistics department wants to evaluate whether the 7 basic topics are beingadequately learned in introductory statistics courses.2. The variables of interest are:•Student•Sex•Pre•test score•Post•test score•Hours per week studyingstatistics3. The measurement scale for each variable:•Student: Nominal•Sex: Nominal•Pre•test score: Interval•Post•test score: Interval•Hours per week studying statistics: Ratio4. Mean of pre•test scores: (4 + 2 + 4 + 3 + 5 + 4 + 2 + 6) /8 = 3.755. Median of post•test scores: (5, 5, 5, 6, 6, 6, 7, 7) → Median = (6 + 6) / 2 = 66. Mode of combined pre and post•test scores: Mode = 57. Range of hours studied: Max•Min = 18•7 = 11

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