Question

A pharmaceutical company has developed a new drug for people with psoriasis, a skin condition. Researchers would like to estimate the proportion of users who saw improvement in their skin after using the drug. Let p represent the true proportion of users whose skin improved. Which of the following is the smallest number of users the researchers can survey to guarantee a margin of error of 0.05 or less at

the 99% confidence level? (Use p^ = 0.5)
a. 600
b. 650
c. 700
d. 750

Answer 1

Answer: 700 (choice C)

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Step-by-step explanation:

At 99% confidence, the z critical value is roughly z = 2.576 which is found using a Z table.

We're given that
`\hat{p} = 0.5` as the sample proportion and E = 0.05 is the desired error.

The min sample size n is:

`n = \hat{p}*(1-\hat{p})\left((z)/(E)\right)^2\\\\n \approx 0.5*(1-0.5)\left((2.576)/(0.05)\right)^2\\\\n \approx 663.5776\\\\n \approx 664\\\\`

Always round up to the nearest integer.

Unfortunately n = 664 isn't one of the answer choices. The next closest value is 700. It appears that your teacher wants to know a valid sample size that is the smallest of the answer choices, not necessarily the smallest ever possible.