Assignment 03

ESTIMATING UNCERTAINTY AND COMPARING DATA TO A STANDARD

This assignment is worth 15 points. Each question is worth 1 point unless otherwise noted.

Copyright EPSY 5261, 2023

Instructions

You will use the sandwiches.csv data set to answer questions in this lab. The data codebook includes a description of how the data were collected and of each of the attributes included in the data.

Use the code chunks in the assignment03.qmd file to load packages, import the data, and carry out any R computations. Submit a PDF document of your responses to the questions in this assignment.

Part 1: Visualizing, Summarizing, and Describing the Sample Data

1. Create a histogram for the sugar attribute. Be sure to update the labels and add a color of your choice. Include your histogram in your document.

2. Use the df_stats() function to compute a set of numerical summary measures for the sugar attribute. Copy-and-paste (or screenshot) the output from this function into the document you will submit. If you copy-and-paste the output into your document, change the font to a monospaced font (e.g., Courier, Consolata).

3. (3pts.) Write a couple of sentences describing the shape, center, and variation of the distribution using the context of the sugar content in sub shop sandwiches.

Part 2: Estimating Uncertainty

Suppose a social scientist carried out a bootstrap simulation (used the do() function similar to how we did in the Day 5 activity) to estimate the standard error of the sample mean amount of sugar. The resulting histogram and summary statistics of this simulation are shown below:

Figure 1: Distribution of 1000 bootstrapped means.

> df_stats(~result, data = bootstrap_means)

  response   min       Q1  median    Q3   max     mean        sd    n missing
1   result 6.592 7.260375 7.49725 7.735 8.775 7.502887 0.3305093 1000       0

4. Explain why we expect the mean of this distribution of sample means to be 7.50.

5. What is the estimated standard error of the means?

6. Explain what the standard error measures using the context.

Part 3: Hypothesis Test to Compare Data to a Standard

The American Heart Association recommends on average no more than ~30g of sugar per day. If we divide this up across three meals a day, the recommended amount for breakfast is 10g. You will use the sugar attribute from the sandwiches.csv data to carry out a hypothesis test to answer the following research question:

Research Question: Is the average amount of sugar in sub shop sandwiches different from the recommended amount of 10g (for a single meal)?

7. Given the research question, please write out the appropriate null and alternative hypotheses that will be tested in words.

8. Given the research question, please write out the appropriate null and alternative hypotheses that will be tested using mathematical symbols.

9. (5pts.) Conduct a hypothesis test using R that allows you to answer the research question. Please be sure to state your conclusions in reference to the hypotheses you wrote out in response to Question 1. To fully answer this question you must:

   • Include the R syntax you used to carry out the test.
   • State the observed sample statistic.
   • State the p-value.
   • State your conclusion and answer the research question (in context).

How do I submit the assignment?

Create a PDF of your responses and submit the PDF via email to both the instructor and TA. Also cc any group members. Before you submit the assignment check that:

• All group members’ names are on the assignment.
• All tables are numbered and have a caption.
• All figures are numbered and have a caption.
• All figures are re-sized to not take up more page space than is necessary to read them.
• No R syntax is included unless the question specifically asked for the syntax to be included. If there is R syntax included, be sure that it is typeset in a monospaced font (e.g., Courier, Inconsolata).
• Do not submit the script file you used unless the directions specifically ask you to submit it.