Confidence Interval for μ, Standard Deviation Estimated (2 of 3)

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The value of t can be determined from a t table. The degrees of freedom for t is equal to the degrees of freedom for the estimate of σ_M which is equal to N-1.

Suppose a researcher were interested in estimating the mean reading speed (number of words per minute) of high-school graduates and computing the 95% confidence interval. A sample of 6 graduates was taken and the reading speeds were: 200, 240, 300, 410, 450, and 600. For these data,

M = 366.6667
s_M= 60.9736
df = 6-1 = 5
t = 2.571

Therefore, the lower limit is: M - (t) (s_M) = 209.904 and the upper limit is: M + (t) (s_M) = 523.430, and the 95% confidence interval is:

209.904 ≤ μ ≤ 523.430

Thus, the researcher can conclude based on the rounded off 95% confidence interval that the mean reading speed of high-school graduates is between 210 and 523.