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1. Suppose in a survey of n = 2000 students, 1200 responded that they prefer small...

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Basic Math

1. Suppose in a survey of n = 2000 students, 1200 responded thatthey prefer small classes and 800 responded that they prefer largeclasses. Let p denote the fraction of all students who preferredsmall classes at the time of the survey, and X ? be the fraction ofsurvey respondents who preferred small classes. (Hint: X isdistributed as a Bernoulli random variable) (a) Show that E(X ?) =p and Var(X ?) = p(1 ? p)/n. (b) Use the survey result to estimatep, and calculate the standard error of your estimator. (Hint:Notice that this is the same as estimating the sample mean)

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