Stat 11 Spring 2011 - Homework 2
(1) For each of the pairs of histograms below, indicate if the left or the right histogram has a larger SD, or if they have the same SD, and briefly explain why. (A sentence for each should suffice.)
(2) The Normal distribution is unimodal-that is, it has only one mode or peak. Not all distributions are unimodal: some may have two or more peaks; see the picture below. Suppose you make a box-plot of a dataset that has two peaks. Could you tell just from looking at the box-plot that the data are not unimodal? Explain briefly.
(3) Suppose scores on a typical IQ test follow approximately a Normal distribution with mean = 100 and SD = 16.
(a) What percent of the people taking the test score below 100? What percent of the people taking the test score between 90 and 110?
(b) An article in Parade magazine reported that Sharon Stone has an IQ of 160. What percent of the people taking the test score above 160?
(c) Ginger takes the test and scores better than all but 25% of people taking the test. What was her test score? In what percentile has Ginger scored?
(4) Let X and Y be Normally distributed variables, with X ∼ N(0,50) and Y ∼ N(0,100). Of the two probabilities P(-20 < X < 20) and P(-20 < Y < 20), which is larger? Explain briefly. (No calculation is necessary.)
(5) While only 5% of babies have learned to walk by the age of 10 months, 75% are walking by 13 months of age. Assuming the age at which babies develop the ability to walk can be described by a Normal model, find the mean and SD.
(6) Go to the web site https://www.stat.uiuc.edu/courses/stat100/cuwu/Games.html and click on "Correlations". Then click on "New Plots" and match the plots to the correlation coefficients. Click on "Answers" when you're done to see how you did. Guess at least three sets of correlations. (You don't need to hand anything in.)
(7) Data Desk. Download the HW2 dataset from
https://www.swarthmore.edu/NatSci/swang1/Stat11. The file is in a compressed (.zip) format; when you double-click on it, it should expand into a Data Desk datafile. (If not, you should download and install the free software Stuffit Expander; google "stuffit expander free download" to find the web page).
(7a) Open the HW2 dataset, which gives the data on US cities we looked at in class. Double-click the cities icon so you can see the list of cities. We will look at whether cities with higher average education levels tend to have higher average incomes. Double-click the HW2 folder to open it. Select the income icon as Y and education icon as X. Then choose Plot > Scatterplots. Do income and education have a roughly linear relationship? Is the relationship positive or negative? Is the relationship strong, moderate, or weak? Print out the plot and hand it in.
(7b) Calculate the correlation of education and income. To do this, click on the HyperView menu of the scatterplot (the triangle in the top left corner of the scatterplot). The correlation coefficient is the number in the bottom left corner of the resulting window.
(7c) Are there any outliers in the scatterplot? If so, which cities are they? To identify points on the plot, use the question mark tool. To select this tool, click on the ? in the tool palettes. (If the tool palettes are not open, select Modify > Palettes to open them.) Then click on each point to identify it. (For this to work, the cities icon must be open.)