STAT 310 - Take Home Final Exam (59 pts.) Due 5/1/08

Problem 1 –“I learned it from watching you Dad!”

Perhaps you have seen the TV commercial where a father is confronting his son about where he learned to smoke marijuana. The script goes something like this:

Father (shaking a cigar box full of pot): Where did you learn to use this stuff?

Son: I learned it from watching you Dad! I learned it from watching you!

This study examines the relationship, if any, between parental drug and alcohol use and the marijuana usage of their college age child. Parents in the study were classified as using neither drugs nor alcohol, one of drugs and alcohol but not both, or finally using both drugs and alcohol. Marijuana usage of the college age student was classified as never using marijuana, occasionally using marijuana, or regularly using marijuana.

A random sample of n = 445 parent/student pairs was taken and each was then classified according to the parents drug & alcohol usage and students marijuana usage, thus both outcomes are random. The contingency table below contains the results.

Parental Use / Never / Occasional / Regularly / Row
Totals
0-Neither / 141 / 54 / 40 / 235
1-One / 68 / 44 / 51 / 163
2-Both / 17 / 11 / 19 / 47
Column
Totals / 226 / 109 / 110 / 445

a) Find thepercentage of college students that regularly use marijuana given that their parents use both drugs and alcohol and contrast it to the percentage of college students that regularly use marijuana given their parents use neither drugs nor alcohol. Discuss your findings. (3 pts.)

b) Use these data to determine if there is a significant relationship between parental drug & alcohol use and the marijuana usage of their college age child. Summarize the results for a general audience. (4 pts.)

c)Fill in the table below using the data from the table on the previous page. (2 pts.)

Parent Drug &
Alcohol Use /
Yes /
No / Row
Total
One or Both
Neither
Column
Total / n = 445

d) Is it valid to calculate a relative risk using these data? Explain. (1 pt.)

e) Use the data in your 2 X 2 table and JMP to find a 95% CI for the relative risk (RR) of having a college age child who uses marijuana associated with parental use of drugs and/or alcohol. What does this CI suggest about the significance the association between parental drug/alcohol use and the marijuana usage of their college age child? Explain.
(3 pts.)

f) Use these data and JMP to find a 95% CI for odds ratio (OR) for having a college age child who uses marijuana associated with parental use of drugs and/or alcohol. What does this CI suggest about the significance the association between parental drug/alcohol use and the marijuana usage of their college age child? Explain. (3 pts.)

Problem 2–Respiration Sinus Arrhythmia in Psychotic Children

Piggot et al. paired 10 psychotic and 10 normal children (controls)by matching them on both age and gender. They compared the subjects for differences in respiratory sinus arrhythmia under conditions of spontaneous and 5-, 10-, and 15-second interval breathing. They recorded the cardiac rate and respiratory changes simultaneously. The table below shows the differences in duration of the cardiac acceleratory phase following the beginning of inspiration (psychotics compared to the controls for the third respiration).

PAIR / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
Psychotic / 1.74 / 1.44 / 2.12 / 1.80 / 2.00 / 2.70 / 1.96 / 1.46 / 1.82 / 1.40
Control / 2.46 / 1.88 / 2.38 / 1.94 / 2.14 / 1.60 / 1.96 / 1.82 / 1.80 / 1.84

Do these data provide sufficient evidence to indicate a difference inthe typical cardiac acceleratory phase for psychotic and normal children? Use the test you feel is most appropriate for answering this question and summarize your findings. (5 pts.)

3 – WinonaHome Sales

These data were collected from a sample of 31 actual home sales in the Winona area. The variables measured on each home sale are listed below. (38 points)
(Datafile: WinonaHomeSales.JMP)

Home sale variables

  • MLS Listing Number – ID number for the listing
  • SellingPrice – actual selling price ($)
  • ListingPrice – price of the home at listing ($)
  • MonthsOnMarket – how long the home was on the market before selling
  • Year – year home was built
  • LotSize – size of lot (acres)
  • TotalSqft = Total square foot of home
  • SqftBelowGround = Total square foot below ground (i.e. basement)
  • GarageSqft = Total Square foot of garage
  • Bedrooms = Number of Bedrooms in home
  • Bathrooms = Number of Bathrooms in home
  • Amenities = Number of amenities listed (e.g. deck, vaulted ceilings, appliances, etc)
  • Appealing = Did the picture of the home look appealing? (0=No, 1=Yes)

Note: this was determined by Shelly Malone, wife of statistics professor

Chris Malone. Chris compiled these data.

Using these data answer the following questions.

a)A home owner who is considering selling their home would like to know on average how long it will take for their home to sell. Use these data to give them answer. (2 pts.)

b)The same individual would like to know how the listing price compares to actual selling price for homes sold in the Winona area. Is there evidence of a significant difference between the two? If so, how large is the difference? Summarize your results. (5 pts.)

c)Is a picture worth thousands of dollars? Shelly Malone classified the picture of the home used in the listing as to whether it was appealing or not. Compare the selling price of homes Shelly found appealing from the picture versus those she did not. Is there a significant difference in the mean selling price? Is so, how large is the difference? (5 pts.)

d)Is there evidence that Shelly simply prefers larger homes? Compare the total square footage of homes Shelly classified as appealing to those she did not. Is there evidence of a significant difference in the mean square footage? Is so, how large is the difference? What are the consequences of this finding as it relates to the findings regarding the mean selling price from part (c)? (5 pts.)

e)Take total square footage into account is there still evidence of a difference in selling price based on Shelly’s assessment of the picture of the home in the listing? Use the appropriate statistical analysis to answer this question and summarize your findings. (4 pts.)

f)Use logistic regression to model the P(Appealing|Total Square Footage). Find the odds ratio for finding the picture of the home appealing associated with a 500 square foot increase in the size of the home. Also use the plot of the logistic fit estimate the probability that Shelly will find a 4000 square foot home appealing based upon the picture. (4 pts.)

g)Treating number of bathrooms as an ordinal variable compare the mean selling price of homes across the different populations of homes based on the number of bathrooms. Which population means significantly differ? (5 pts.)

h)Develop a regression model for selling price using the following potential predictors: year, lot size, total square footage, square footage below ground, garage square footage, number of bedrooms, number of bathrooms, number of amenities, and appeal of listing picture. Which predictors are in your “final” model? What is the R-square? Do the regression assumptions appear to be satisfied for your model? (6 pts.)

i)Use your model from part (h) to predict the selling price of the following home:

A 4300 total square footage, 4 bedroom, 3.5-bath home built in 2000 on 1.2 acre lot. This home also has a 1200 square footage below ground, 10 amenities, a 1100 square foot garage, and Shelly found the picture in the paper appealing. (2 pts.)

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