Answerl 5. A physician wants to estimate the proportion of her patients that hav

Question

Answerl 5. A physician wants to estimate the proportion of her patients that have high blood pressure. (a) The physician wants to be 90% confident that her sample estimate is within ± 10% of the actual population proportion, what is the minimum sample size that she should select to achieve her goals? [5 points) Answer (b) Suppose that the physician selects a sample of 80 patients and finds 24 of them have high blood pressure. Calculate a 99% confidence interval to estimate the proportion of all her patients that have high blood pressure. [5 points] Answer (Please give eacn endpoint.)

Explanation / Answer

1) At 90% confidence interval the critical value Z0.95 = 1.645

margin of error = 0.1

Or, Z0.95 * sqrt(P * (1 - P)/n) = 0.1

Or, 1.645 * sqrt(P * (1 - P)/n) = 0.1

Or, sqrt(P * (1 - P)/n) = 0.1/1.645

Or, sqrt(P * (1 - P)/n) = 0.061

Or, n = P * (1 - P)/(0.061)2

Or, n = P * (1 - P)/0.004

B) n = 80

P = 24/80 = 0.3

At 99% confidence interval the critical value is Z0.995 = 2.58

The cinfidence interval is

P +/- Z0.995 * sqrt(P * (1 - P)/n)

= 0.3 +/- 2.58 * sqrt(0.3 * 0.7/80)

= 0.3 +/- 0.132

= 0.168, 0.432

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