Question

A sample of 245 observations is selected from a normal population with a population standard deviation of 25. The sample mean is 20.

Determine the standard error of the mean. **(Round your
answer to 3 decimal places.)**

Determine the 90% confidence interval for the population mean.
(Use *z* Distribution Table.) **(Round your answers to
3 decimal places.)**

Answer #1

Given that,

Point estimate = sample mean =
= 20

Population standard deviation =
= 25

Sample size = n =245

At 90% confidence level

= 1-0.90% =1-0.90 =0.10

/2
=0.10/ 2= 0.05

Z/2
= Z_{0.05 = 1.645}

Margin of error = E = Z/2
* (
/n)

= 1.645 * ( 25 / 245
)

**Standard error = 1.597**

= 1.645*1.597

=2.627

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

- E <
<
+ E

20 - 2.627 < <
20 + 2.627

17.373<
< 22.627

**(17.373 ,22.627 )**

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