We are collecting data on the patients that have been vaccinated for the coronavirus, and the initial data shows a 90% success. We want the margin of error to be no more than 3%. We want to be extremely careful, so we are going to use a 99% confidence. Determine the smallest size of the sample to achieve this level of confidence. a. 560 b. 680 c. 664 d. 600 e. 686

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We are collecting data on the patients that have been vaccinated for the coronavirus, and the initial data shows a 90% success. We want the margin of error to be no more than 3%. We want to be extremely  careful, so we are going to use a 99% confidence. Determine the smallest size of the sample to achieve this level of confidence.  a. 560  b. 680  c. 664  d. 600  e. 686

Drood1980 · Accepted Answer

Step 1  Given: The initial data shows a 90% success. We want the margin of error to be no more than 3%. We want to be extremely  careful, so we are going to use a 99% confidence.   Step 2  Sample size  n=(zα2E)p(1−p), where zα2 is the critical value of the normal distribution and p is the 90% initial success, E is the mariginal error.  p=0.90  E=0.03  99% confidence interval and the remaining interval is 1%.so we will take here α=0.01  As a result zα2=2.58  n=(2.580.03)20.90(1−0.90)  =66.56×10  ≈665.6  Therefore the correct option is (c) 664.

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