Question

A simple random sample of size n is drawn. The sample​ mean, x is found to be 17.7​, and the sample standard​ deviation, s, is found to be 4.8. Construct a 95% confidence interval about μ if the sample​ size, n, is 35.

Answer 1

Let be a random sample of size drawn from a normal distribution with mean and standard deviation . A % confidence interval of is given by . Here . So = the upper 0.025 point of a t distribution with 34 degrees of freedom. Hence the confidence interval is [16.05114, 19.34886] .

X1 X2

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100(1 c

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ta/2,n-1, Xn+ta/2,n-1

35, T17.7,s 4.8, a 0.05 n

to.025,34 2.032245