In this question, you will construct bootstrap confidence intervals using the Smiles dataset.

Please download this dataset from Learn to answer the following questions.

The Smiles dataset contains results from an experiment that studied the effects of smiling and leniency in judging students accused of cheating. The population parameter of interest

is a difference in means s - n, where s and n are the average leniency scores for smiling students and students with neutral expression, respectively.

In answering the questions below make sure you use appropriate notation where necessary.

(i) Find the best point estimate for the difference in means.

(ii) Use StatKey to generate a bootstrap distribution of 10,000 differences in sample means. Please include your bootstrap distribution in your assignment solutions.

(iii) Describe the shape and centre of your bootstrap distribution in one or two sentences.

(iv) Using percentiles from your bootstrap distribution, find and interpret in context a 90% confidence interval for the difference in means in one or two sentences.

(v) At 90% confidence, is it plausible that smiling has no effect on leniency? Justify your answer in one or two sentences.

(vi) Repeat parts (iv) and (v) replacing 90% confidence with 99% confidence.

Leniency Group

7 smile 3 smile 6 smile 4.5 smile 3.5 smile 4 smile 3 smile 3 smile 3.5 smile 4.5 smile 7 smile 5 smile 5 smile 7.5 smile 2.5 smile 5 smile 5.5 smile 5.5 smile 5 smile 4 smile 5 smile 6.5 smile 6.5 smile 7 smile 3.5 smile 5 smile 3.5 smile 9 smile 2.5 smile 8.5 smile 3.5 smile 4.5 smile 3.5 smile 4.5 smile 2 neutral 4 neutral 4 neutral 3 neutral 6 neutral 4.5 neutral 2 neutral 6 neutral 3 neutral 3 neutral 4.5 neutral 8 neutral 4 neutral 5 neutral 3.5 neutral 4.5 neutral 6.5 neutral 3.5 neutral 4.5 neutral 4.5 neutral 2.5 neutral 2.5 neutral 4.5 neutral 2.5 neutral 6 neutral 6 neutral 2 neutral 4 neutral 5.5 neutral 4 neutral 2.5 neutral 2.5 neutral 3 neutral 6.5 neutral