Lorraine computed a confidence interval for based on a sample of size 41. Since

Question

Lorraine computed a confidence interval for based on a sample of size 41. Since she did not know , she used s in her calculations. Lorraine used the normal distribution for the confidence interval instead of a Student's t distribution. Will her interval be longer or shorter than one obtained by using an appropriate Student's t distribution? Explain.

Shorter. For d.f. = 40, zc is greater than tc.Shorter. For d.f. = 40, zc is less than tc.    Longer. For d.f. = 40, zc is less than tc.Longer. For d.f. = 40, zc is greater than tc.

Explanation / Answer

The formula for confidence interval for mean is
Statistic +/- ME
Where ME is marginal error
ME = z-value * sigma/sqrt(sample size)
In this case sample size is large so we can compute the CI without sigma.

the answer is: shorter. for d.f.=40, zc is less than tc, and the resulting margin of error E is smaller.

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