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Lesson_05_sol_sample_distr

# Lesson_05_sol_sample_distr - Sampling Distributions...

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Sampling Distributions – Solutions 1 Suppose that medical researchers want to estimate the true proportion of all teenagers with high blood pressure whose blood pressure would decrease if they took calcium supplements. To test this, they plan a clinical trial in which n = 200 teenagers with high blood pressure will be given calcium supplements. a. Suppose the clinical trial is completed, and 120 of the 200 participants experienced a decrease in blood pressure. i. What is the value of the sample proportion (also called the point estimate) p ˆ for this sample? p ˆ = 120/200 = 0.60 ii. Using the result found in part i, determine the value of the standard error of p ˆ . Note that in many situations we will not know the true parameter, p, and thus will substitute our sample proportion for p in the calculation of the SE. This formula then for the SE( p ˆ ) when p is unknown is: n ) p ˆ 1 ( p ˆ SE( p ˆ ) = 200 ) 4 . 0 ( 6 . = 0.035 iii. Verify that normal approximation methods would be appropriate for this study.

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