From a sample of 25 graduate students, the mean number of months of work experience prior to entering an MBA program was 33.59. The national standard deviation is known to be 1…

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asked Sep 23, 2021 39.1k views

1 Answer

Cwehrung · Answer 1 · 2021-09-27T22:41:07+0000

Answer:

The 90% confidence interval for the population mean is between 27.34 months and 39.84 months.

Explanation:

We have that to find our
$\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = (1-0.9)/(2) = 0.05$

Now, we have to find z in the Ztable as such z has a pvalue of
$1-\alpha$ .

So it is z with a pvalue of
1-0.05 = 0.95 , so
z = 1.645

Now, find the margin of error M as such

$M = z*(\sigma)/(√(n))$

In which
$\sigma$ is the standard deviation of the population and n is the size of the sample.

M = 1.645*(19)/(√(25)) = 6.25

The lower end of the interval is the sample mean subtracted by M. So it is 33.59 - 6.25 = 27.34 months

The upper end of the interval is the sample mean added to M. So it is 33.59 + 6.25 = 39.84 months

The 90% confidence interval for the population mean is between 27.34 months and 39.84 months.