A sample with a sample proportion of 0.4 and which of the following sizes will produce the widest 95% confidence interval when estimating the population parameter?A.55B.45C.35D.65SUBMITarrow_backPREVIOUS
Question
A sample with a sample proportion of 0.4 and which of the following sizes will produce the widest 95% confidence interval when estimating the population parameter?A.55B.45C.35D.65SUBMITarrow_backPREVIOUS
Solution
The width of a confidence interval is determined by the standard error of the estimate, which is inversely proportional to the square root of the sample size. This means that the larger the sample size, the smaller the standard error, and thus the narrower the confidence interval. Conversely, the smaller the sample size, the larger the standard error, and thus the wider the confidence interval.
Therefore, out of the given options (55, 45, 35, 65), the smallest sample size will produce the widest 95% confidence interval. So, the answer is C.35.
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