Math – Statistics Exam

92.283 Introduction to Statistics

Name:_____________________________________

Exam 2

October 22, 2012

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1. A news article by Reuters reported:

In a new study, Dr Matti Uhari and colleagues at the University of Oulu in Finland, randomly gave 857 healthy children in daycare centers xylitol in syrup, gum or lozenge form, or a placebo gum, syrup or lozenge in five doses per day for 3 months. According to a report in the October issue of the Journal of Pediatrics, the incidence of ear infections were reduced by 40% in children given xylitol chewing gum, 30% in those given syrup and 20% in those given lozenges when compared to children give a placebo.

a. Is this an observational study or a randomized experiment?

b. If this is an experiment, what are the three criteria in this case?

c. What are the explanatory and response variables?

d. If it is an experiment, diagram the randomized comparative experiment.

2. A news article on the Reuters Health website reported that:

A study of over 1200 people over age 65 showed that the “owls” – those who tend to go to sleep after 11 p.m. and rise after 8 a.m. – tend to be as healthy and intelligent as “larks” – those who go to bed before 11 p.m. and rise before 8 a.m. – according to a report in the December 19/26 issue of the British Medical Journal . The researchers found that owls tend to have higher average income than the larks.

a. Is this an observational study or a randomized experiment?

b. What are the explanatory and response variables?

3. The faculty senate at a large university wanted to know what proportion of the students thought a foreign

language should be required for all students. A simple random sample of 500 students was selected. A survey form was sent to each of these 500 students by e-mail.

a. What is the population of interest to the faculty senate?

b. What is the sample?

c. What is the variable under consideration?

4. The following scatterplot shows the increase in Halloween candy sales (in millions

of dollars) over a 7-year period.

Scatter Plot

Simple linear regression results:
Dependent Variable: Candy Sales
Independent Variable: Year
Candy Sales = -178.09921 + 0.090035714 Year
Sample size: 7
R (correlation coefficient) = 0.9875
R-sq = 0.9752395
Estimate of error standard deviation: 0.03394944
Parameter estimates:

Parameter

Estimate

Intercept

-178.09921

Slope

0.090035714

a. Looking at the scatterplot of the data, what does it tell you about the relationship between the year and the amount of candy sales?

b.
Find the equation of the least squares line of regression.

c. What does the correlation coefficient tell you about the relationship between the year and the amount of candy sales?

d. Predict the amount of sales for 2012.

e. Are you confident that predictions based on the equation of the least squares line of regression will be quite accurate? Why or why not?

f. What percent of the variation in the amount of candy sales can be explained by the regression on (relationship with) the year?