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#### ST 352 R Tutorial Assignment 5 Analysis of Categorical Data 20 points Problem: You participated in a “memory game” activity

###### Statistics

ST 352

R Tutorial Assignment 5

Analysis of Categorical Data

20 points

Problem: You participated in a “memory game” activity. In this problem, you will answer this question of interest: “Is there an association between the time of day when the activity was performed and how many items were remembered?” Use the memorygame data set posted on Canvas to answer this question of interest. Note: the number of items remembered is categorized into two groups. The data set will contain two columns: column 1 is the time of day the activity was performed (“time”) and column 2 is whether or not at least 60% of the items were remembered (“pctremember”):

• time (time of day you performed the activity: “early” or “late”)

• pctremember (“yes” = remembered at least 60% of the items, “no” = remembered less than 60% of the items)

1. (2 points) Construct a table of counts and a table of proportions (with appropriate comparison proportions to answer the question of interest). Use R to obtain these tables, but do NOT copy and paste those tables into your assignment. Instead, use the tables from R to construct your own table where you include both the counts and proportions (or percentages) in the same table.

Table of Counts

 evening morning <= 60% remembered 14 31 At least 60% remembered 14 21

Table of Proportions

 evening morning <= 60% remembered 0.5000 0.5962 At least 60% remembered 0.5000 0.4038

2. (2 points) Based on the proportions in #1, does it appear that the proportion remembering at least 60% of the items is different between those who performed the activity in the morning and those who performed the activity in the evening? Briefly explain.

3. (3 points) State the null and alternative hypotheses in statistical notation. Define the notation in the context of the problem.

4. (2 points) Report the expected counts for all cells in the table. Are the expected counts “large enough” for conclusions from the chi-square test to be valid to the population? Briefly explain.

5. (2 points) Report the chi-square statistic with degrees of freedom and the p-value here.

6. (4 points) Answer the question of interest in the context of the problem.

7. (5 points) Report and interpret the 95% confidence interval for the difference in the population proportion remembering at least 60% of the items between those who did the activity in the morning (labeled “early” in the data set) and those who did the activity in the evening (labeled “late” in the data set): (pearly – plate)

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