Question

In: Statistics and Probability

Given a sample mean of 12.5 based on 25 cases and a population variance of 10,...

Given a sample mean of 12.5 based on 25 cases and a population variance of 10, construct a 95% confidence interval for the population mean. Interpret the resulting interval.

Expert Solution

Solution :

Given that,

= 12.5

² = 10 = = 3.16

n = 25

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.960

Margin of error = E = Z_/2* ( $\sqrt$ /n)

= 1.960 * (3.16 / $\sqrt$ 25 ) = 1.24

At 95% confidence interval estimate of the population mean is,

- E < < + E

12.5 - 1.24 < < 12.5 + 1.24

11.26 < < 13.74

(11.3, 13.7)

orchestra answered 2 years ago

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