Question

In: Statistics and Probability

a sample of 245 observations is selected from a normal population for which the population standard...

a sample of 245 observations is selected from a normal population for which the population standard deviation is known to be 25. the sample mean is 20. determine the standard error of the mean. determine the 90% confidence interval for the population mean.

Expert Solution

Solution :

Given that,

= 20

= 25

n = 245

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

The standard error of the mean = ( $\sqrt$ /n)

= 25 $\sqrt$ 245

The standard error of the mean = 1.6

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

= 1.645 * (25 / $\sqrt$ 245) = 2.6

At 90% confidence interval estimate of the population mean is,

- E < < + E

20 - 2.6 < < 20 + 2.6

17.4 < < 22.6

(17.4 , 22.6)

orchestra answered 2 years ago

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