Hi,

I need some help on the theory questions in statistics. The questions are related to identifying response variables, factor, level, blocks, confounding factors etc for statistical experiments and also comparing the conditions of a statistical experiment. There are no calculations involved. Lot of theory.

Module 5, Topic 2 Practice Problems Problem 1 Suppose that you have data from a simple comparative experiment in which there are 1 observations from group 1 and 2 observations from group 2. In 1 = 2 = n then there are two possible ways to compute confidence intervals for the data, one in which the two groups are independent of each other and one is which the data is paired and from common blocks. The following are the two confidence interval formulas for the two situations. 1 1) 1 2 1 + 2 2 ( ) + 1 2) 1 2 1 Suppose that n = 10. In this case the t value for a 95% confidence interval using formula 1) is 18 = 2.10 and the t value for a 95% confidence interval using formula 2) is 9 = 2.26. In addition, the value of .4472 in formula 1) and the value 1 10 1 10 + 1 10 = = .3162 in formula 2). Compare these two formulas. Under what conditions is the 95% confidence interval in 2) shorter than the 95% confidence interval in 1)? Note that the value will be the same as the value 1 2 since the mean of all the differences will be the same as the difference between the two means. Problem 2 Nine samples were taken from 2 streams, four from one and five from the other and the following data were obtained. Pollution lever in stream 1: ppm Pollution level in stream 2: ppm 16 9 12 10 14 8 11 6 5 Module 5, Topic 2 Practice Problems Someone claimed that the data proved that stream 2 is less polluted than stream 1. Someone else asked the following questions: When were the data collected? Were the data collected all in one day or on different days? Were the data collected during the same time period for the two streams? What was the temperature in the two streams when the data was collected? At what points in the two streams were the data collected? Why do you think the second person asked these questions? Are there other questions that should be asked? Is there any set of answers to these questions and others that you can think of that would justify the use of a confidence interval formula to draw conclusions from this data? Problem 3 Sixteen judges rated two randomly allocated brands of diet cola according to taste (scale 1 to 10) as follows. Brand A Brand B 2 8 4 3 2 5 1 3 9 7 9 7 2 4 2 4 a) What formula would you use to find a 95% confidence interval for the difference in the population mean test score for Brand A minus Brand B. b) The mean score for Brand A = 3.88 and the standard deviation of the scores for Brand A = 3.27. The mean score for Brand B = 5.13 and the standard deviation of the scores for Brand B = 1.96 find a 95% confidence interval for the difference in population mean taste scores. c) Can you think of a better way to conduct this experiment. Write out precise instructions for the way to carry out what you suggest. Problem 4 Suppose that you are interested in the amount of wear that will occur on four different brands of automobile tires. In addition suppose that you have six different cars and six different drivers. You will conduct the following experiment: You will equip each car with one each of the four tire brands. Each of the six cars will be driven by the same driver for the same number of miles. After the required number of miles has been driven the amount of tread remaining on each tire will be measured. The following table lays out the data for this experiment. The blanks in the table will be filled in with the remaining tread on the tires. Brand 1 Car and driver 1 Car and driver 2 Brand 2 Brand 3 Brand 4 Module 5, Topic 2 Practice Problems Car and driver 3 Car and driver 4 Car and driver 5 Car and driver 6 a) For this experiment what is the response? b) For this experiment what is the factor? What are the levels for this factor? c) For this experiment what are the blocks? d) List possible nuisance variables for this experiment? e) It is recommended that the brand of tire should be randomly assigned to the four possible positions on each car. Why is this important? Problem 5 More people get colds during cold weather than during warm weather. Does this prove that cold temperatures cause people to get colds? What are potential confounding factors? Problem 6 The Pygmalion effect is psychology refers to a situation where the high expectations of a supervisor or teacher translate into improved performance by subordinates or students. It is a case of the self-fulfilling prophecy. The following experiment was conducted to determine if the Pygmalion effect was occurring in a military situation. Ten companies of soldiers in an army training camp were selected for the study. Nine of the companies had three platoons and one had two platoons. Each platoon has its own platoon leader. Using a random mechanism, one of the platoons was selected to be the Pygmalion platoon. The randomization was conducted separately for each company. Prior to assuming command of their platoons, each leader met with an army psychologist. For all of the Pygmalion platoon leaders the psychologists described a nonexistent battery of tests that had predicted superior performance for his or her platoon. At the conclusion of basic training, soldiers took a battery of tests. The Practical Specialty Test evaluated soldiers on their ability to operate weapons and answer questions about their use. The average scores on the Practical Specialty Test for the soldiers in the different platoons is in the following table. The purpose of this experiment is to find out if the Practical Specialty Test scores are different for the Pygmalion platoons than the control platoons. Treatments Company Pygmalion Platoon Control Platoon 1 80.0 63.2 69.2 2 83.9 63.1 81.5 Module 5, Topic 2 Practice Problems 3 68.2 76.2 4 76.5 59.5 73.5 5 87.8 73.9 78.5 6 89.8 78.9 84.7 7 76.1 60.6 69.6 8 71.5 67.8 73.2 9 69.5 72.3 73.9 10 83.7 63.7 77.7 a) For this experiment what is the response? b) Are there any blocks in this experiment? If so what defines the blocks? c) What is the factor in this experiment? How many levels are there for this factor