My budget for the study has been increased so that i can take a sample of 7200 rather than the sample of 800 i was oringinally going to take! Consider the situation described in the image above. The result of this is that their confidence interval will now be: about 3 times wider pretty much unchanged about 1/9 as wide about 1/3 as wide about 9 times widertheir confidence interval will now be:
Question
My budget for the study has been increased so that i can take a sample of 7200 rather than the sample of 800 i was oringinally going to take! Consider the situation described in the image above. The result of this is that their confidence interval will now be: about 3 times wider pretty much unchanged about 1/9 as wide about 1/3 as wide about 9 times widertheir confidence interval will now be:
Solution
The confidence interval will now be about 1/3 as wide. This is because the width of a confidence interval is inversely proportional to the square root of the sample size. So, if you increase your sample size from 800 to 7200 (which is 9 times larger), the width of your confidence interval will be divided by the square root of 9, which is 3. Hence, the confidence interval will be about 1/3 as wide.
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