14B InClass

According to a study done by the National Survey of Student Engagement, on average, college students spend 17 hours per week preparing and studying for their classes.[1][2]

Several people gathered around a table with papers, a computer, and other work materials.

Credit:iStock/golero

Question 1

1) Do you think students with different majors (specifically arts and humanities, STEM, education, and business) differ in the mean number of hours they spend preparing for class each week? Explain.

Question 2

2) Use the previous scenario to answer the following questions.
Part A: What is the question being posed?
Part B: How many groups are being compared?
Part C: Which variable are you comparing between the groups?
Part D: Define what each parameter represents.𝜇1=𝜇2=𝜇3=𝜇4=

Question 3

3) Write the null and alternative hypotheses.

Suppose a college randomly sampled 12 students from each of the four major departments at the college and asked them how many hours per week they spend studying and preparing for class. The data are given in the following table.

Arts and Humanities STEM Education Business
16 18 14 16
18 20 18 20
17.5 18.5 16 15.5
19 22 15.5 14
15 18 16.5 12
17.5 20.5 17 12
15.5 16.5 13 15
19.5 14 19 16.5
21 17 15 17.5
14 19 16 17
18 23 20 15
16.5 16 12 18
We will now use technology to find the summary statistics for each group. These will be the same steps we use to run an ANOVA. For this activity, we will assume the data meet the assumptions for ANOVA. We will learn about assumptions for ANOVA in the next in-class activity.
1. Go to the DCMP ANOVA: Analysis of Variance tool at https://dcmathpathways.shinyapps.io/ANOVA.
2. In the “Enter Data” box, choose “Provide Own.”
3. Enter the name for the response variable—“Hours Studying per Week.”
4. Choose the number of groups. In this case, we have four groups.
5. Type in the names(majors, in this case)for each group.
6. Copy and paste the data above into each data box.

Question 4

4)Looking at just the descriptive statistics, do you think there is a difference in the mean number of hours spent studying for each major? Explain.

Question 5

5) We will now create box plots so that we can visually assess the data. Under “Type of Plot,”choose “Boxplot.”
Part A: Looking at the boxplots, what differences and similarities do you see in the groups?
Part B: Based solely on the visual evidence, what do you predict the conclusion of the hypothesis will be?

Question 6

6)We will now draw our attention to the ANOVA table. State the F-statistic and the P-value.

Question 7

7)Using a significance level of 5%, what is the conclusion? Refer back to the research question and interpret the results in the context of the problem.

Question 8

8) Suppose a friend concluded from the previous ANOVA table that the mean number of study hours was significantly different between all four majors. Would this be a correct interpretation based on the ANOVA results? Explain.

Question 9

9) Suppose instead of a significance level of 5%, the significance level is 1%. Would you come to the same conclusion as in Question 8? Explain.

  1. Aaron.(2014, July 24). Which college majors study the most?MyMajors. https://www.mymajors.com/blog/college-majors-study/ ↵
  2. Survey Instruments. (2013). National Survey of Student Engagement. https://nsse.indiana.edu/nsse/survey-instruments/index.html ↵