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A randomized comparative experiment studied the effect of diet on blood pressure

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A randomized comparative experiment studied the effect of diet on blood pressure. Researchers divided 54 healthy white males at random into two groups. One group received a calcium supplement, and the other group received a placebo. At the beginning of the study, the researchers measured many variables on the subjects. The average seated systolic blood pressure of the 27 members of the placebo group was reported to be X = 114.9 -0.1*(position of your first letter in the alphabet) with a standard deviation of s = 9.3. For example, if our last name starts with A then x would be 114.8. 1. A) Give a 95% confidence interval for the mean blood pressure of the population from which the subjects were recruited. (hint: make sure that you use the proper equations for sample mean and not for sample proportion) 1. B) The recipe you used in part (a) requires an important assumption about the 27 men who provided the data. What is this assumption? Question 2 5 pts A researcher studied the effect of an antidepressant on depression. He randomly assigned subjects with moderate levels of depression to two groups. One group received the antidepressant and the other a placebo. Subjects were blinded with respect to the treatment they received. After four weeks, the researcher interviewed all subjects and rated the change in their symptoms based on the comments of subjects during the interview. Critics said that the results were suspect because the ratings were not blind. Explain what this means and how lack of blindness could bias the reported results. Question 3 20 pts Three friends Michael, John, and Natalia are roommates and argue which route is faster from their dorm to the University, Michael argues that taking the train is faster. John argues that it is faster to take the bus and Natalia is sure that biking to campus is faster. A) Design an observational study that tests the claims. State specifically how you are going to recruit, what instructions you are going to give your recruits, what is your sample size, and how you are going to take measurements. B) Design an experiment. State specifically how you are going to recruit, what instructions you are going to give your recruits, what is your sample size, and how you are going to take measurements. C) State three lurking variables. Which design A or B ensures that the lurking variables have an equal impact on the choices? Question 4 15 pts An agency of the federal government plans to take an SRS of residents in each state to estimate the proportion of owners of real estate in each state's population. The populations of the states range from about 563,600 people in Wyoming to about 37.3 million in California, according to the 2010 U.S. census. A) Will the variability of the sample proportion change from state to state if an SRS of size X * 1000 is taken in each state? X is the position of your last letter in the alphabet. Explain your answer. B) Will the variability of the sample proportion change from state to state if an SRS of 1/10 of 1% (0.001) of the state's population is taken in each state? C) Assuming that the population parameter p is the same and does not change from state to state. Assume that p=20%. Calculate the probability that the sample proportion p-hat is 21% based on the sample size you determined in answer A. (bonus question 5 points) Question 5 20 pts A company in the food industry grows and sells chickens. The company assigned newly laid chicken eggs to one of three temperatures: hot, neutral (room temperature), or cold. Here are the data on the number of eggs and the number that hatched. The cost per egg to establish a cold, neutral and hot environment is the last column in the table. Number Temperature of Eggs Hatched Cost Cold 27 ? $0 Neutral 56 38 $1 Hot 104 75 $2 Where X is the position of your last name in the alphabet. A) Does temperature affect hatching? Show your calculations and explain using data. B) If the price of buying an unhatched egg is $0.5 and the cost of selling a newly hatched chicken is $5 which temperature should the company use? C) (Bonus 10 points) Based on the information given in B what is the expected profit per egg?

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