Before conducting a study it is often a good idea to decide on the necessary sample size. To do so, statisticians often first decide on anacceptable margin of error and then work backward to the sample size. Since they haven't run the study yet it is common practice to approximate thesample proportion as 50% since this is the worst case scenario.Recall that the standard eror for a single proportion isSE =P(1-p)Note: The calculation to find the sample size will likely give a decimal answer so be sure to round appropriately so that the actual margin of error will beless than what the researchers want.(a) If researchers decide on a 4.2% margin of error for a 95% confidence interval. What sample size should they pursue?(b) If researchers decide on a 2.8% margin of error for a 99% confidence interval. What sample size should they pursue?

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Description: Before conducting a study it is often a good idea to decide on the necessary sample size. To do so, statisticians often first decide on anacceptable margin of error and then work backward to the sample size. Since they haven't run the study yet it i

From provided information, Sample proportion is (p̂) = 50% i.e. 0.5 The sample size can be…

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(a) If researchers decide on a 4.2% margin of error for a 95% confidence interval. What sample size should they pursue? If researchers decide on a 2.8% margin of error for a 99% confidence interval. What sample size should they pursue?

(a) If researchers decide on a 4.2% margin of error for a 95% confidence interval. What sample size should they pursue? If researchers decide on a 2.8% margin of error for a 99% confidence interval. What sample size should they pursue?

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Before conducting a study it is often a good idea to decide on the necessary sample size. To do so, statisticians often first decide on an
acceptable margin of error and then work backward to the sample size. Since they haven't run the study yet it is common practice to approximate the
sample proportion as 50% since this is the worst case scenario.
Recall that the standard eror for a single proportion is
SE =
P(1-p)
Note: The calculation to find the sample size will likely give a decimal answer so be sure to round appropriately so that the actual margin of error will be
less than what the researchers want.
(a) If researchers decide on a 4.2% margin of error for a 95% confidence interval. What sample size should they pursue?
(b) If researchers decide on a 2.8% margin of error for a 99% confidence interval. What sample size should they pursue?

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