Q1. The “High School and Beyond” data set”hsb2.csv”. The National Center of Education Statistics conducted a Survey of high school seniors collecting test data on reading writing and several other subjects. Here we examine a simple random sample of 200 students from this survey:
- Conduct side-by-side box plots of reading and writing scores.
- Condcut an inference test to find out if there is a clear difference between the average scores on the two exams.
- Are the reading scores and writing scores correlated?
- Draw a plot to show whether they were correlated, e.g., a xyplot will show the trend.
Q2. The EPA data set (file epa_final.txt). Each year the US Environmental Protection Agency releases fuel economy data cars manufactured that year. The data file includes random samples of course with manual an automatic transmission manufactured in 2012. We use miles per gallon (mpg) to measure the fuel efficiency. Please use the column “transmission_desc” to determine whether a car is automatic or manual.
- Using “city_mpg”, draw a histogram for cars with manual transmissions & histograms for cars with automatic transmission, respectively
- Conduct an inference test to determine if there is a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage. (the column city_mpg). Assume that the conditions for inference are satisfied
- For cars with manual transmissions is there evidence that there is a difference between the fuel efficiency in city or on highway conduct an inference test to prove it.
Q3. Researchers studying anthropometry collected body girth measurements and skeletal diameter measurements, as well as age, weight, height and gender for 507 physically active individuals, (data file: bids.txt) in the desert both height and shoulder growth or measured in centimeters.
- Draw a plot to explore the relationship between height (column name “hgt”) and shoulder girth column name (“sho.gi”). Describe from the following three aspects: the relationship, the trend, and the variation.
- Fit in regression model to determine if shoulder girth can be used to predict height.
Q4. Use the same data set in Q3 and explore the relationship between weight (column name “wgt” measured in kilogram) and hip girth (column name “hip.gi”, measured in centimeters.)
- Fit regression model to describe the relationship between hip girth and weight.
- Conduct an inference test to determine if hip girth is a significant predictor of weight.
- How would the relationship change if weight was measured in pounds while the unit for hip girth remained in centimeters?
Q5. Time magazine reported the result of a telephone pole with 800 adult Americans to question posed but of the Americans who were surveyed was: “should the federal tax on cigarettes be raised to pay for healthcare reform?” The results of a survey were:
Is there sufficient evidence at the alpha = 0.05 level to conclude to conclude that the two populations -- smokers and non-smokers -- differ significantly with respect to their opinions?
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