In: Statistics and Probability
Suppose the goal is to estimate the parameter stated in question 3 using a 90% confidence interval with margin of error no larger than 0.039. What is the minimum number of colleges and universities that would need to be selected to allow the calculation of a 90% confidence interval with margin of error no larger than 0.039? It can be assumed for this problem only that the proportion of all colleges and universities that will be moving their summer 2020 classes online is 0.21 and this number can be used for this problem .
The following information is provided,
Significance Level, α = 0.1, Margin of Error, E = 0.039
The provided estimate of proportion p is, p = 0.21
The critical value for significance level, α = 0.1 is 1.64.
The following formula is used to compute the minimum sample size
required to estimate the population proportion p within the
required margin of error:
n >= p*(1-p)*(zc/E)^2
n = 0.21*(1 - 0.21)*(1.64/0.039)^2
n = 293.36
Therefore, the sample size needed to satisfy the condition n
>= 293.36 and it must be an integer number, we conclude that the
minimum required sample size is n = 294
Ans : Sample size, n = 294 or 293
If you take z value upto 3 or 4 deciamal answer would be
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