Task:

In this exercise, we will explore a dataset that includes the safety inspection scores for restaurants in the city of Austin, Texas. We will be interested in determining the average restaurant score for the city from a random sample of the scores; the average restaurant score is out of 100. We’ll compare two methods for computing a confidence interval for that quantity: the bootstrap resampling method, and an approximation based on the Central Limit Theorem.

Question 1

Complete the function one resampled mean below. It should take in an original table data, with a column Score, and return the mean score of one resampling from data.

Question 2

Complete the function bootstrap scores below. It should take no arguments. It should simulate drawing 5000 resamples from restaurant sample and compute the mean restaurant score in each resample. It should return an array of those 5000 resample means.

Question 3

Compute a 95 percent confidence interval for the average restaurant score using the array resampled means

Question 4

What distribution is the histogram between question 2 and 3 displaying (that is, what data are plotted), and why does it have that shape?

Question 5

Does the distribution of the sampled scores look normally distributed? State “yes” or “no” and describe in one sentence why you should expect this result.

Question 6

Without referencing the array resampled means or performing any new simulations, calculate an interval around the sample mean that covers approximately 95% of the numbers in the resampled means array. This confidence interval should look very similar to the one you computed in Question 3.

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