STAT 200 Questions (Looking for someone who is good with statistics.)

Stat 200 Project 1 2017b Name _____

Instructions: For best readability, print this document from a PDF viewer, not a web-browser. Printing directly from a website often omits details or changes the fonts. Click "download", then "open" to automatically load the PDF into a viewer. If your work computer is blocked from printing, use another (such as the Umuc Lab)

Fill in the parts below and turn in the completed 2-page document at a face-to-face class. With prior approval you may scan and email it (as a PDF or images) to avoid missing the due date.

To facilitate grading, this project print-out should be completed manually (writing / marking). It could be completed using a PDF editor as long as the 2-page limit and format remain. It's also possible to complete it with a word-processor but attach the entire PDF as a cover sheet (single or double-sided paper).

1 A real-life example of hypothesis testing using the Chi-square distribution. The problem described here: http://www.robweir.com/blog/2010/02/microsoft-random-browser-ballot.html

involves a computer programming error (later fixed), which distorted the choices when picking among 5 browsers. Each browser should be appearing about 1/5th of the time in positions 1 – 5 on the ballot. Read the site thoroughly as it already answers the questions below. Use the Chi-square table as needed.

a) State the null-hypothesis and the alternative-hypothesis (in words or symbols)

b) What is the expected (E) number of times each browser should appear in each position? = ___ c) Find the degrees-of-freedom (df) for the Chi-square test, = ___

Bonus 1 (+0.5%) How did the website get this number? (fill in the correct df formula)

d) If alpha = 0.005, what is the chi-square Critical value? = ___ (use the table) e) What are the website's chi-square Test values for Internet Explorer? = ___ f) ...& for Firefox? = ___ g) What is the result of the hypothesis test? h) Why does that indicate the initial version of the balloting software was faulty?

2 Graph of electric car usage in Germany, 2010

a) Estimate the modal distance __ b) How many trips (in %, approximate) correspond to this distance? __ c) Does the graph imply there are any 100+ km commutes by electric car? (explain why)

d) Draw a line on the horizontal axis where the median (commuting distance) is most likely to be e) What (approximate) % of commutes are more than 37 km? __ f) Is the distribution left or right-skewed?

3 The claim that "rising oil prices are bad for stocks" sounds plausible. If it is valid, then a) the anticipated correlation is (pick 1): positive negative none b) So when oil prices rise, stock prices (in general) should do what? __

Search for "monthly oil prices" and "monthly stock indexes". Select 1 of the better-known oil price benchmarks & likewise select a major index of stock prices (or use an index of Oil Company stocks). Obtain the last 2 (or 3) years worth of oil & stock data (include & count back from the latest month available). Place the info in a spreadsheet with headings for Date (Mo, Yr), Oil, Index (or similar titles). Synchronize it so data for the same months matches up on the same row.

List the oil (stock) indexes you used, along with the periods selected in each, & their sources c) name: name:

d) From ___ to ___ From ___ to ___

e) web address: web address:

Find the correlation (r) using the spreadsheet's built-in function (or use a linear regression app) =correl(data_1, data_2) ← data_1, data_2 are ranges like A1:A10, B1:B10, etc

f) The calculated correlation (r) = ___ g) How does this r compare with the expected correlation (in part c)? h) What does it indicate about the accuracy of the claimed connection between oil & stock prices? i) So, based on the actual correlation, if oil prices rise what should happen to stocks? __

Bonus 2 (+0.5) Is the correlation in (f) significant? Report the hypothesis test results using the Pearson PMC r table for both values of α shown. (include the df, and critical values for each α):

4. This site: www.sense.bc.ca/research.htm presents info about speed-related crashes. a) In each box, what does the unshaded part represent? Box 1:

Box 2:

Box 3:

b) If their numbers are correct, are the illustrations? Explain briefly for each box.

Box 1:

Box 2:

Box 3:

c) For Box 3, if its corner square is the correct size, what about the 2-5% numbers? Explain.