Investigation 1: Distances from birthplace (assigned Thur, Jan 7, due Tues Jan 12)

You may work with one other person on this assignment, handing in one report with both names. Word-processed reports are much preferred to hand-written ones. Please copy/paste relevant, well-labeled Minitab output into a Word file as appropriate.

Recall that you told me whether or not you were born in California and how many miles Cal Poly is from where you were born. These data (in miles) are in the Minitab worksheet birthplaces.mtw. [Click on the link to open the file, as long as you are working on a PC computer with Minitab software. You can use Minitab in any PC lab on campus, and you can find instructions for downloading Minitab to your own PC here.]

a) Produce (and submit) a bar graph of the “born in CA?” variable. [Hint: Choose Graph> Bar Chart. Select the “Simple” option and click OK. Then double click on “c1 born in CA?” to make that appear in the “Categorical variables” box. Then click on “Chart Options” and select “Show Y as Percent.” Click OK, and then click OK again. Once the graph appears, copy/paste it into your Word file.] Also comment on what this graph reveals.

b) Determine the sample proportion of students who were born in California. [Hint: Choose Stat> Tables> Tally Individual Variables. Select the appropriate column/variable, and also click on “Percents” in addition to “Counts.”]

c) Consider determining a confidence interval for the population proportion of Cal Poly students who were born in California. Check and comment on whether the technical conditions for this confidence interval procedure are satisfied.

d) Produce a 90%, 95%, and 99% confidence interval for the population proportion of Cal Poly students who were born in California. [Hint: You could do the calculations by hand, but it’s easier to use Minitab: As we have done in class, choose Stat> Basic Statistics> 1-Proportion.] Also write a sentence interpreting what the 95% CI reveals.

e) Produce (and submit) a histogram and boxplot of the distances from birthplace. [Hint: Choose Graph> Histogram. Select the “Simple” option and click OK. Then double click on “c2 miles from home” to make that choice appear in the “Graph variables” box. Click OK again. Once the graph appears, copy/paste it into your Word file. Then repeat with Graph> Boxplot.] Describe what these graphs reveal about the distribution of these distances, and also explain why the graphs are not all that informative.

f) Determine and report the mean and standard deviation of the distances from birthplace. Also determine and report the five-number summary and inter-quartile range. [Hint: As we have done in class, choose Stat> Basic Statistics> Display Descriptive Statistics.]

I think that the maximum distance (17,330) was reported erroneously, because the circumference of the earth is about 25,000 miles, so no point on the earth can be more than 12,500 miles away from any other point. I suspect that this student mistakenly reported distance in kilometers rather than in miles. Assume that my suspicion is correct for the rest of this assignment.

g) Use an online conversion calculator, such as here, to convert the maximum value (17,330) from kilometers to miles. Make this change in the Minitab worksheet, and then re-calculate the statistics in f). Identify which statistics have changed substantially and which have not.

h) Consider determining a confidence interval for the population mean distance from birthplace among all Cal Poly students. Check and comment on whether the technical conditions for this confidence interval procedure are satisfied.

i) Produce a 95% confidence interval for the population mean distance from birthplace among all Cal Poly students. [Hint: You could do the calculations by hand, but it’s easier to use Minitab: As we have done in class, choose Stat> Basic Statistics> 1-Sample t….] Also write a sentence summarizing what this 95% CI reveals.

j) Determine how many, and what proportion, of the 83 students in the sample reported a distance that falls within this confidence interval. Is this proportion close to .95? Should it be close to .95? Explain.

k) Now consider only the distances for those students who were born in California (c5). Produce (and submit) a histogram and boxplot of these distances from birthplace. Describe what these graphs reveal about the distribution of these distances.