$\text { Find the required sample size without making a guess for the observed value of } \hat { p } \text {. }$
-A researcher wishes to estimate the proportion of all drivers who exceed the speed limit on a certain stretch of road where accidents frequently happen. Obtain a sample size that will ensure a
Margin of error of at most 0.021 for a 98% confidence interval.
A)65
B)3078
C)28
D)1321

Question

$\text { Find the required sample size without making a guess for the observed value of } \hat { p } \text {. }$
-A researcher wishes to estimate the proportion of all drivers who exceed the speed limit on a certain stretch of road where accidents frequently happen. Obtain a sample size that will ensure a
Margin of error of at most 0.021 for a 98% confidence interval. 
A)65
B)3078
C)28
D)1321

Quizplus · Accepted Answer

The sample size needed to achieve a margin of error of 0.021 for a 98% confidence interval is 3078. This can be calculated using the formula: n = (Z^2 * p * q) / e^2, where Z is the z-score for the desired confidence level, p is the estimated proportion of drivers who exceed the speed limit, q is the complement of p (1-p), and e is the margin of error. Since we do not have an estimate for p, we can use the conservative estimate of p = 0.5, which will give us the largest possible sample size. Plugging in the values, we get: n = (2.326^2 * 0.5 * 0.5) / 0.021^2 = 3078.

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$\text { Find the required sample size without making a guess for the observed value of } \hat { p } \text {. }$