Part I - Short Answer (10 marks)

1.

(1 mark) True or False: For samples of size 2 or more, the standard deviation of the sampling distribution for the mean is always smaller than the standard deviation of the population from which the sample was drawn.
Solution: This is actually true since $\sigma/\sqrt{n} < \sigma$ when $n\geq 2$ where $\sigma/\sqrt{n}$ is the sd of the sampling distribution of the mean. However, this question is based on material from Ch. 4.

2.

(1 mark) Consider the following scatterplot relating women's height (in inches) and weight (in pounds).

Briefly, what is the biggest problem in using this information to predict the weight of a woman who is 65 inches tall and is 65 years old.
Solution: Such a prediction would be an example of extrapolation.

3.

(1 mark) Which of the following is FALSE if a distribution is skewed to the right.

(a)

the first quartile is farther from the median than the third quartile

(b)

the mean is the centre of mass of the distribution

(c)

about 50% of the observations are less than the mean

(d)

roughly 25% of the observations are less than the first quartile

(e)

the mean is bigger than the median

Solution: Because of a typo, there are actually two false statements here, (a) and (c).

4.

(1 mark) Which of the following statements is FALSE about the following histogram:

(a)

The mean should be higher than the median.

(b)

There may be one or more outliers.

(c)

The inter-quartile range is about $15000 to $70000.

(d)

The median looks to be about $30000.

(e)

The distribution is skewed to the right.

Solution: (c), this range clearly contains more than the middle half of observations.

5.

(1 mark) To examine the effect of pets in stressful situations, researchers would like to recruit 45 women who are dog lovers to participate in a study. Which of the following recruiting methods is the BEST of the available choices?

(a)

A researcher stands outside a pet store and asks women to participate in the study.

(b)

Researchers contact women on campus who have taken part in fund raising for a local animal shelter.

(c)

A list of phone numbers for dog owners is obtained from dog licensing records. Owners are contacted at random and women owners are asked to participate.

Solution: (c) is the best way to avoid selection bias.

6.

(1 mark) In a toxicology experiment, rats are exposed to bus exhaust at a number of high concentrations. Lung function is measured on the rats before and after exposure. The researchers describe their results and the implications for lung function in humans. This is an example of

(a)

the Hawthorne effect

(b)

nonresponse bias

(c)

extrapolation

(d)

the placebo effect

(e)

using aggregate data to draw conclusions

Solution: (c)

7.

(1 mark) The following scatterplot examines the relationship between speed and stopping distance for cars.

Based on how the data are plotted, what is the response and what is the explanatory variable?
Solution: Stopping distance is the response and speed is the explanatory variable.

8.

(1 mark) Refer to the previous scatterplot. True or false: A linear model appears reasonable for these data.
Solution: I would say a linear model is reasonable.

9.

(2 marks) Refer to the data from the previous two questions. Some summary statistics from the dataset are given below.

mean of speed = 15.4   sd of speed = 5.29
mean of distance = 43.0   sd of distance = 25.8
correlation between distance and speed

What are the least squares estimates of the slope and intercept for a simple linear regression line fit to the scatterplot from question 7.
Solution: There was a typo on the exam and the correlation got left out. It is 0.8068949. This gives a slope of $25.8/5.29 \times 0.807 = 3.94$ and an intercept of $43.0 - 3.94 \times 15.4 = -17.7$.