# Analyzing Puzzle Completion Time for History and Mathematics Majors

## Use Excel for Data Analysis

**Final answer:** The psychologist conducted a study to compare the ability of history majors and mathematics majors to solve different types of puzzles. The mean time to complete each puzzle type by major can be plotted using a line graph in Excel. Additionally, statistical tests such as ANOVA can be performed to determine if there is an interaction effect and if the mean completion time differs between puzzle types for each major. Excel can be used for data analysis and visualization.

## Explanation:

The psychologist conducted a study to compare the ability of history majors and mathematics majors to solve different types of puzzles. The study included 25 mathematics majors and 25 history majors from a liberal arts college in Maine. Each major had five students randomly assigned to one of the following puzzle types: crossword puzzle, cryptogram, logic problem, maize, and cross sums.

The time taken to complete each puzzle was recorded, and a penalty of 10 minutes was added for incomplete or incorrect puzzles. To analyze the data, we can plot the mean time to complete a puzzle for each type by major using a line graph in Excel.

## a) Line Graph:

Using Excel, create a line graph with the puzzle types on the x-axis and the mean time to complete a puzzle on the y-axis. Plot two lines, one for history majors and one for mathematics majors. This graph will visually represent the differences in mean completion time for each puzzle type between the two majors.

## b) Interaction Effect:

To determine if there is an interaction effect between major and puzzle type, we can perform a statistical test at the 0.05 level of significance. This test will help us understand if the effect of the puzzle type on completion time differs between history majors and mathematics majors.

## c) One-Way ANOVA:

If an interaction effect is present, we can conduct a one-way ANOVA to test whether the mean time to complete a puzzle for history majors depends on the type of puzzle, and whether the mean time to complete a puzzle for mathematics majors depends on the type of puzzle. This test will help us determine if there are significant differences in mean completion time between puzzle types for each major.

Perform the one-way ANOVA tests at a level of significance of 0.05 using Excel. This analysis will provide insights into the relationship between major, puzzle type, and completion time.

Use Excel. Assume that a psychologist conducted a study to determine whether there are differences between the ability of history majors and mathematics majors to solve various types of puzzles. Twenty-five mathematics majors and 25 history majors were randomly selected from the students at a liberal arts college in Maine. Five students from each major were randomly assigned one of the following puzzles: a crossword puzzle, a cryptogram, a logic problem, a maize and a cross sums. The time in minutes (rounded to the nearest minute) was recorded for each student in the study. If a student could not complete a puzzle in the maximum time allowed, or completed a puzzle incorrectly, then a penalty of 10 minutes was added to his or her time. The results are shown in the file Puzzle. a) Using a line graph, plot the mean time to complete a puzzle for each type by major. b) At the 0.05 level of significance, is there an interaction effect? c) If interaction is present, conduct a one-way ANOVA to test whether the mean time to complete a puzzle for history majors depends on the type of puzzle. Does the mean time to complete a puzzle for mathematics majors depends on the type of puzzle? Conduct the one-way ANOVA tests at a level of significance of 0.05. Use Excel. The psychologist conducted a study to compare the ability of history majors and mathematics majors to solve different types of puzzles. The mean time to complete each puzzle type by major can be plotted using a line graph in Excel. Additionally, statistical tests such as ANOVA can be performed to determine if there is an interaction effect and if the mean completion time differs between puzzle types for each major. Excel can be used for data analysis and visualization.