1. Write a short definition for each of the following:Outlier,Correlation,Parameter
An outlier is a variable value that lies outside the normal range for the distribution. You can use the 1.5 IQR rule to judge whether or not a particular value is an outlier. Correlation is a measure of the strength and direction of the linear relation between two variables. A parameter is a value for a variable that is associated with a particular population. Often the exact value is difficult to determine, so it has to be estimated by a statistic taken from a sample of the population.
2. During the imperial period, Roman legionaries were required to be at least 68 inches tall. During that period, adult males had an average height of 65 inches with a standard deviation of 4.5 inches. Assuming that heights follow a normal distribution, what percentage of the male population could meet or exceed the height requirement?
74.86% is below this level, so approximately 25% of the adult male population was this tall.
3. The plot below shows age in years and asking price in thousands of dollars for a number of used Honda Accords listed for sale in a newspaper.
 |
For this data set υx = 5.17 years, ¤x = 3.27 years, υy = $5,800, ¤y = $3,790, and r = -0.79. Given that 
and 
, predict the asking price of a 7 year old car.
4. A local gym offers the option of using a personal trainer to its members. For an extra monthly fee, a member can meet with a personal trainer every two weeks. Their progress is evaluated and the trainer makes suggestions on the member's exercise program that are designed to help them achieve their fitness goals. The owners of the gym survey the members and find that after several months those members who chose to use a personal trainer showed greater improvement in fitness level than those who did not. Why is the conclusion of this study suspect? Describe the design of an experiment that you could do to study the relationship between the use of a personal trainer and improvement in fitness.
For a sample or an experiment to be valid, the two groups being compared have to be as much alike as possible with the exception of the factor being studied. The result of the owners' study is suspect because the two groups are self-selected. Quite possibly the members willing to pay extra to use a personal trainer are more highly motivated to succeed on average than the members who don't use a trainer. To correct this imbalance, the owners would have to randomly assign members to the two groups and use a large enough sample to even out the fluctuations that would naturally occur. A reasonable experiment would divide, say, 100 members into two groups at random. The first group would act as a control and would not get access to assistance from personal trainers. The second group would be given access to a trainer free of charge. You could use a simple coin flip to assign the members to groups. Alternatively you could use a list of 100 members numbered from 0 to 99 and read off number blocks of size two from the random number table until you found 50 members to go into the first group.