Question

During a blood-donor program conducted during finals week for college students, a blood-pressure reading is taken first, revealing that out of 300 donors, 42 have hypertension. All answers to three places after the decimal.

1.The probability, at 60% confidence, that a given college donor will have hypertension during finals week is_____ with a margin of error of 0.017

2.Using a prior estimate of 15% of college-age students having hypertension, how many donors must we examine in order to be 99% confident that we have the margin of error as small as 0.01.?

Answer 1

Part )

p̂ = X / n = 42/300 = 0.14
p̂ ± Z(α/2) √( (p * q) / n)
0.14 ± Z(0.4/2) √( (0.14 * 0.86) / 300)
Z(α/2) = Z(0.4/2) = 0.842
Lower Limit = 0.14 - Z(0.4) √( (0.14 * 0.86) / 300) = 0.123
upper Limit = 0.14 + Z(0.4) √( (0.14 * 0.86) / 300) = 0.157
60% Confidence interval is ( 0.123 , 0.157 )
( 0.123 < P < 0.157 )

Part 2)

p̂ = 0.15
q̂ = 1 - p̂ = 0.85
Critical value Z(α/2) = Z(0.01/2) = 2.5758
n = ( Z(α/2)2 * p̂ * q̂ )/e2
n = ( Z(0.01)2 * 0.15 * 0.85)/ 0.012
n = 8460

Required sample size at 99% confident is 8460.