Reading A recent Gallup poll asked Americans to disclose the n...

Question

Reading A recent Gallup poll asked Americans to disclose the number of books they read during the previous year. Initial survey results indicate that s = 16.6 books.

c. What effect does doubling the required accuracy have on the sample size?

Accepted Answer

Welcome back, everyone. A health study estimates the standard deviation of daily step counts as S equals 9.8. The minimum number of participants required to estimate the mean daily steps within two steps with 99% confidence is found to be and equals 160. What effect does doubling the required accuracy have on the sample size? The sample size will double the sample size will remain the same. The sample size will increase by a factor of 4, and D, the sample size will be halved. For this problem, let's remember the minimum sample size formula and minimum is equal to the critical z value multiplied by the standard deviation S divided by the margin of error E and where squaring the whole fraction. So if we distribute the square, we can show that n minimum is equal to z2s quad divided by e2. In this problem we're keeping the same standard deviation. We're using the same confidence of 99%, and the only parameters that change are N and E. So we can just say it's some constant k divided by Esquared. And because K is a constant. We can just show that if we take one minimum sample size and its corresponding margin of error, then the product between N and E is going to be constant. We can show that N1 multiplied by E12 is going to be equal to N2 multiplied by E22, right, for two conditions, 1 and 2. So what we want to do is simply find the ratio between N2 and N1. So if we rearrange this equation, and 2 divided by N1 is going to be equal to E12 divided by E22, or basically E1 divided by E2. Squared So in this problem, we understand that. E1 divided by E2 is going to be equal to 2, right? Because according to the problem, it says that what effect does doubling the required accuracy have on the sample size. So we're doubling the required accuracy, which means that the ratio of the margins of error, specifically E1 divided by E2, is equal to 2. So we're going to get 2 squad which is equal to 4, and now we have shown that the new sample size N2 is equal to 4 multiplied by N1, right? So the new sample size will increase by a factor of 4, which corresponds to the answer choice C. Thank you for watching.

Reading A recent Gallup poll asked Americans to disclose the number of books they read during the previous year. Initial survey results indicate that s = 16.6 books.c. What effect does doubling the required accuracy have on the sample size?

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Reading A recent Gallup poll asked Americans to disclose the number of books they read during the previous year. Initial survey results indicate that s = 16.6 books.
c. What effect does doubling the required accuracy have on the sample size?