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(b)Explain the concept of confounding in the context of this study. Include an example of a possible confounding variable.(c)If the mean number of new cavities for those who ate an apple a day was statistically significantly smaller than the mean number of new cavities for those who ate less than one apple a week, could one conclude that the lower number of new cavities can be attributed to eating an apple a day? Explain.
2001 Free Response: Students are designing an experiment to compare the productivity of two varieties of dwarf fruit trees. The site for the experiment is a field that is bordered by a densely forested area on the west (left) side. The field has been divided into eight plots of approximately the same area. The students have decided that the test plots should be blocked. Four trees, two of each of the two varieties, will be assigned at random to the four plots within each block, with one tree planted in each plot.The two blocking schemes shown below are under consideration. For each scheme, one block is indicated by the white regions and the other block is indicated by the gray region in the figures.(a)Which of the blocking schemes, A or B, is better for this experiment? Explain your answer.(b)Even though the students have decided to block, they must randomly assign the varieties of trees to the plots within each block. What is the purpose of this randomization in the context of this experiment?2005 Free ResponseSurvey will be conducted to examine the educational level of adult heads of households in the United States. Each respondent in the survey will be placed into one of the following two categories:Does not have a high school diplomaHas a high school diplomaThe survey will be conducted using a telephone interview. Random-digit dialing will be used to select the sample.(a)For this survey, state one potential source of bias anddescribe how it might affect the estimate of the proportion of adult heads of households in the United States who do not have a high school diploma.(b)A pilot survey indicated that about 22 percent of the population of adult heads of households do not have a high school diploma. Using this information, how many respondents should be obtained if the goal of the survey is to estimate the proportion of the population who do not have a high school diploma to within 0.03with 95 percent confidence? Justify your answer.(c)Since education is largely the responsibility of each state, the agency wants to be sure that estimates are available for each state as well as for the nation. Identify a sampling method that will achieve this additional goal andbriefly describe a way to select the survey sample using this method.Free ResponseAn oil and gas company has a four story buildings downtown with each floor having 16 rooms. Engineering is on the first floor, meteorology is on the second, geology and chemistry on the third and administration on the fourth. A third party consulting firm has been hired to evaluate worker job satisfaction. Describe how to implement each of the following sampling techniques.a.Convenience sampleb.Simple random samplec.Cluster random sampled.Stratified random samplee.Systematic random samplef.Voluntary response sample