In August 2021, data analysts examined the prices of 20 food items at Trader Joe's and Lunds & Byerlysto examine which grocery store was more affordable for students. The grocery list was the same for both stores, and the current price (including sale's prices) were used. In this assignment, you will use the data provided to answer the following research question:

Is there a difference in average affordability between Lund's and Trader Joe's?

Each question is worth 1point unless otherwise indicated.

Explore the Observed Data

Open thegrocery.tpfile in TinkerPlots. a single plot of the observed data to compare the prices between Lund's and Trader Joe's. Also include the numerical mean values for each food list on the plot.

1. Copy-and-paste (or sketch) the plot of the observed data, with the averages included, into your word-processed document.

Use the groups' mean values to compute thedifference in means for the two groups. Subtract the Trader Joe averagefromthe Lunds average.

1. Report the observed difference in means.

1. What does the observed result (the difference in means) suggest about the answer to the research question? Explain.

1. Why do you need to conduct a simulation in order to determine whether Lund's or Trader Joe's is more affordable for students? Explain why you cannot answer the research question using just the observed result.(2pts)

Bootstrap Test

1. null hypothesis for the bootstrap test.

Set up a TinkerPlots sampler to generate different bootstrap samples of the data under the model specified in the null hypothesis (Hint: You did something similar to this in theMurderous Nurseactivity).

1. Copy-and-paste (or sketch) a picture of the TinkerPlots sampler window into your word-processed document.

1. What repeat value did you use for your sampler? Explain why you chose this value.

1. Did you usewith orwithout replacement for the prices in the sampling device? Explain your choice.

1. Did you samplewith orwithoutreplacement for the group labels (Lund's or Trader Joe's) in the sampling device? Explain your choice.

Simulate using the Model

Use TinkerPlots to carry out 500 trials of the bootstrap simulation. plot of the 500 bootstrapped differences in means.

Evaluate the Observed Results

1. Describe the shape of the distribution of the 500 simulated results. Also compute and report the mean and standard deviation of this distribution.

1. Explain, by referring to the null hypothesis, why we could have expected the mean you computed in Question #10.

Add a reference line to the plot of the distribution of the 500 simulated results at the value of the difference in theobserved data.

1. Copy and paste (or sketch) the plot (with the reference line) into your word-processed document.

1. Use the plot from Question #12, to compute thep-value. Show your work.

Answer the Research Question

Based on thep-value you computed, how compatible is the observed difference in means with the results produced by the model specified in the null hypothesis? What does this suggest about the answer to the research question? Explain.(2pts)