Question: (15 points) Suppose that a researcher obtained the following random sample of exam grades for 20 students taking statistics at SPSU, to attempt to estimate the true mean score of statistics students at the university.

1. Create a histogram of the exam data.
2. Which type of study is this (select all that apply)?
   1. Observational study
      ii. Designed experiment, but not double blind
      iii. Designed, double blind, experiment
      iv. A matched pairs experiment
3. If the students in the class were now each offered 5 bonus points for taking a course survey and EVERY student did the survey and got the credit, which of the following would happen to our sample (select all that apply):
   1. The mean would increase by 5
   2. The mean would increase, but by less than 5
   3. The median would increase by 5
   4. The median would increase, but by less than 5
   5. The interquartile range would increase
   6. The standard deviation would increase
4. Suppose you are going to create a confidence interval with the data from this study. Which of the following would reduce the margin of error the MOST?
   1. Take a smaller sample, so that the sample mean may be lower and the margin of error will be smaller as well.
   2. Take a larger sample. With more data our estimate is expected to be more accurate, leading to a smaller margin of error.
   3. Stay with the current sample size. This sample size was used for a reason, which was most likely to reduce the margin of error.
   4. We cannot tell from the information provided.

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