Exercises

Section 11.5 Exercises

Checkpoint 11.5.1.

This exercise deals with an experiment that was conducted among students. The aim of the experiment was to assess the effect of rumors and prior reputation of the instructor on the evaluation of the instructor by her students. The experiment was conducted by Towler and Dipboye

Towler, A. and Dipboye, R. L. (1998). The effect of instructor reputation and need for cognition on student behavior (poster presented at American Psychological Society conference, May 1998).

. This case study is taken from the Rice Virtual Lab in Statistics. More details on this case study can be found in the case study "Instructor Reputation and Teacher Ratings" that is presented in that site.

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The experiment involved 49 students that were randomly assigned to one of two conditions. Before viewing the lecture, students were give one of two "summaries" of the instructor’s prior teaching evaluations. The first type of summary, i.e. the first condition, described the lecturer as a charismatic instructor. The second type of summary (second condition) described the lecturer as a punitive instructor. We code the first condition as "C" and the second condition as "P". All subjects watched the same twenty-minute lecture given by the exact same lecturer. Following the lecture, subjects rated the lecturer.

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The outcomes are stored in the file "teacher.csv". The file can be found on the internet at http://pluto.huji.ac.il/~msby/StatThink/Datasets/teacher.csv. Download this file to your computer and store it in the working directory of R. Read the content of the file into an R data frame. Produce a summary of the content of the data frame and answer the following questions:

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Identify, for each variable in the file "teacher.csv", the name and the type of the variable (factor or numeric).
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Estimate the expectation and the standard deviation among all students of the rating of the teacher.
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Estimate the expectation and the standard deviation of the rating only for students who were given a summary that describes the teacher as charismatic.
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Construct a confidence interval of 99% confidence level for the expectation of the rating among students who were given a summary that describes the teacher as charismatic. (Assume the ratings have a Normal distribution.)
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Construct a confidence interval of 90% confidence level for the variance of the rating among students who were given a summary that describes the teacher as charismatic. (Assume the ratings have a Normal distribution.)
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Checkpoint 11.5.2.

Twenty observations are used in order to construct a confidence interval for the expectation. In one case, the construction is based on the Normal approximation of the sample average and in the other case it is constructed under the assumption that the observations are Normally distributed. Assume that in reality the measurement is distributed \(\mathrm{Exponential}(1/4)\text{.}\)

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Compute, via simulation, the actual confidence level for the first case of a confidence interval with a nominal confidence level of 95%.
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Compute, via simulation, the actual confidence level for the second case of a confidence interval with a nominal confidence level of 95%.
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Which of the two approaches would you prefer?
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Checkpoint 11.5.3.

Insurance companies are interested in knowing the population percent of drivers who always buckle up before riding in a car.

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When designing a study to determine this proportion, what is the minimal sample size that is required for a 99% confident that the population proportion is accurately estimated, up to an error of 0.03?
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Suppose that the insurance companies did conduct the study by surveying 400 drivers. They found that 320 of the drives claim to always buckle up. Produce an 80% confidence interval for the population proportion of drivers who claim to always buckle up.
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