standard deviation prior to taking the sample that will be used to develop an es

Question

standard deviation prior to taking the sample that will be used to develop an estimate of the population mean. So technically we don't mean that or is actually known with certainty. we just mean that we obtained a good estimate of the standard deviation prior to sampling and thus we won't be using the same sample to estimate in the denominator, a larger sample size interval, and greater precision. The inter for determining the size of a simple ill edure lly we don't mean provide a smaller margin of error, a proced sample necessary to obtain a desired is discussed in Section 8.3 Exercises Methods I. A simple random sample of 40 items resulted in a sample mean of 25. The population standard deviation is 5. What is the standard error of the mean, At 95% confidence, what is the margin of error? b.

Explanation / Answer

Data given is as follows:

Sample size, n = 40

Sample mean, m = 25

Standard deviation, S = 5

(a)

Standard error of the mean, also called as the standard deviation of the sampling distribution, is determined using the following formula:

SE = S/(n^0.5) = 5/(40^0.5) = 0.79

(b)

For 95% confidence interval, the critical z-score is:

zc = 1.96

The formula for margin of error is:

ME = zc*SE

Put the values above:

ME = 1.96*0.79 = 1.548

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