About This Assignment

This mini project covers Chapters 1 and 2 and uses the wrangling of data and ideas related to basic sampling distributional theory. You will be tasked with answering a challenging word problem and be asked to show your work on the next assignment page by submitting an HTML file.

Format: numeric answer "quiz"
Time limit: none
Number of attempts: 3

Academic Integrity

Getting help from your peers is not permitted.
Collaborating, or completing the quiz with others in the class, is not permitted.
Copying or reusing previous work is not permitted.
Open-book research for the quiz is permitted and encouraged.

Speed of Light

Introduction

(From MS 2.84) Speed of light from galaxies. Astronomers theorize that cold dark matter (CDM) caused the formation of galaxies. The theoretical CDM model requires an estimate of the velocity of light emitted from the galaxy. The Astronomical Journal (July, 1995) published a study of galaxy velocities. One galaxy, named A1775, is thought to be a double cluster; that is, two clusters of galaxies in close proximity. Fifty-one velocity observations (in kilometers per second, km/s) from cluster A1775 are in the GALAXY 2 File.

> head(gal)
# A tibble: 6 x 1
  VELOCITY
     <dbl>
1    22922
2    20210
3    21911
4    19225
5    18792
6    21993

Calculation

Use an RMD document to include the following answers:

Use a graphical method to describe the velocity distribution of galaxy cluster A1775. ( Note if you use hist() explore the options to help the plot)
Examine the graph, part a. Is there evidence to support the double cluster theory? Explain.
Calculate numerical descriptive measures (e.g., mean and standard deviation) for galaxy velocities in cluster A1775. Depending on your answer to part b, you may need to calculate two sets of numerical descriptive measures, one for each of the clusters (say, A1775A and A1775B, use side-by-side boxplots with a formula in the argument) within the double cluster. (Please note that this will require some wrangling of the data -- you may use [] or the dplyr package)
Suppose you observe a galaxy velocity of 20,000 km/s. Is this galaxy likely to belong to cluster A1775A or A1775B? Explain.
Using the unclustered data (51 values) how many measured velocities were within 1 standard deviation of the mean?

Now answer the following quiz question.