You are measuring the height and weight of 100 people in a clinical trial using inches and pounds as the unit of measurement. You then compute summary statistics such as the mean, median, and standard deviation of height and of weight, and the correlation between height an
1. You are measuring the height and weight of 100 people in a clinical trial using inches
and pounds as the unit of measurement. You then compute summary statistics such as
the
between height and weight. For all of the following questions, assume that the people in
the trial were selected using a simple random sample.
a. You notice after the fact that all weight measurements were made using a scale
that was incorrectly calibrated. Five pounds were systematically added to every
weight measurement. To ensure that you have correct summary statistics, which
of the four summary statistics, mean, median, standard deviation and correlation,
do you need to recompute, and which do you not need to recompute?
b. Some collaborators in the trial are based in the United Kingdom, where they use
measurements in the units of centimeters and kilograms. You need to present
them with summary statistics using those measurement units. Which of the four
summary statistics, mean, median, standard deviation and correlation, do you
need to recompute using the required 1 units, and which do you not need to
recompute?
c. You may assume that the population distribution of height is
Tell me if each of the following statements is true or false.
i. When viewed as a random variable, the sample mean of height follows
the normal distribution
ii. The population mean of height is always equal to the population median
of height.
iii. The sample mean of height is always equal to the sample median of
height.
iv. The maximum likelihood estimate of the population standard deviation of
height is unbiased.
2. After computing a 95% confidence interval for the population mean of height you show it
to a colleague. She says that the confidence interval has a 95% probability of containing
the true population mean of height. Is she right?
3. Tell me if each of the following statements is true or false.
a. The law of large numbers says that as the sample size increases the distribution
of the sample mean of weight will become closer and closer to the normal
distribution.
b. When performing simple univariate linear regression, the slope of the regression
line after regressing height on weight is always the same as the slope of the
regression line after regressing weight on height.
c. If a father whose height is far above average has a son whose height is barely
above average, this can be explained by the regression effect.
d. The distribution of the sample standard deviation of height follows the t
distribution with the number
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