Study 1: A researcher was interested in whether pain tolerance levels were related to hair color. 80 people were selected from a group of volunteers, 20 with light blonde hair, 20 with dark blond hair, 20 brunettes and 20 redheads. The subjects underwent a series of tests and pain tolerance scores (on a scale of 0 to 100) were assessed.

Study 2: A technician is interested in the effects of using different baking temperatures on the impact strength of particle board. 20 boards are randomly allocated to 20 different baking temperatures. After the boards are baked, they are sent to a laboratory where the impact strengths are measured.

Study 3: The manager of an auto repair shop is interested in whether using a new diagnostic machine will speed up the regular servicing of cars. There are two mechanics working on regular services, one with 8 years experience while the other mechanic had only 2 years experience. One mechanic was told to use the diagnostic machine on the next 10 cars she serviced, but not use it on the following 10 cars. The other mechanic was told not to use the diagnostic machine on the next 10 cars he serviced, but to use it on the following 10 cars. Each mechanic recorded the time it took to complete the services for each of these jobs.

Study 4: A sociologist is interested in comparing the exam results for male and female students on 10 different subjects. The proper authority was contacted to obtain the numbers of male and female students who took the exam and the numbers of male and female students who got each of the grades A, B, C and D.
 

• For each study, describe what treatment is being compared and what response is being measured to compare the treatments.
• Which of the studies would be described as experiments and which would be described as observational studies?
• For the studies that are observational, could an experiment have been carried out instead? If not, briefly explain why not.

42, 47, 46, 35, 43, 39, 38, 40, 50, 37, 68, 37, 47, 44, 49
41, 34, 38, 41, 36, 42, 38, 38, 58, 34, 32, 42, 49, 52.
 

• Order the data in increasing order. Construct a histogram plot of the data.
• Calculate the five number summary for the data (min, lower quartile, median, upper quartile and max). Note: If there are x indices of numbers below the mean then the (x+1)/2 -st number in the ordered observations, gives you the value of the lower quartile. The upper quartile is computed identically as the lower quartile, except that you take the value of the observation half-way between the mean and the max-observation.
• Using your plots, in plain English, briefly comment on the data and the story the above summary/plots convey.