Suppose the number of business majors at liberal arts colleges are normally distributed and have a known population standard deviation of 21 students and an unknown population mean. A random sample of 35 liberal arts colleges is taken and gives a sample mean of 420 business majors. Find the margin of errorfor the confidence interval for the population mean with a 90% confidence level. Round the final answer to two decimal places.

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04-07-2020
Mathematics

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Suppose the number of business majors at liberal arts colleges are normally distributed and have a known population standard deviation of 21 students and an unknown population mean. A random sample of 35 liberal arts colleges is taken and gives a sample mean of 420 business majors. Find the margin of errorfor the confidence interval for the population mean with a 90% confidence level. Round the final answer to two decimal places.

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joaobezerra joaobezerra · Answer 1 · 2020-07-04T04:37:17+02:00

Answer:

The margin of error for the confidence interval for the population mean with a 90% confidence level is of 5.84 business majors.

Step-by-step explanation:

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

[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]

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

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

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

In this question:

[tex]\sigma = 21, n = 35[/tex]

So

[tex]M = z*\frac{\sigma}{\sqrt{n}} = 1.645*\frac{21}{\sqrt{35}} = 5.84[/tex]

The margin of error for the confidence interval for the population mean with a 90% confidence level is of 5.84 business majors.

vg2121 vg2121 · Answer 2 · 2021-10-30T03:32:51+02:00

Answer:

5.838

Step-by-step explanation:

To find the margin of error we need to identify three things: the z-score, σ, and n.

1.Find zα2 using invNorm. The invNormfunction has one input: probability.

Here, α=1−0.90=0.10. Probability is then 1−0.102=0.95. To find our z-score, we select invNorm after pressing 2nd then VARS. Type invNorm(0.95). The output Is 1.6448. This is the z-score.

2. σ=21.

3. n=35.

4. We type 1.6448×2135√ on the calculator. The output is 5.838, when rounded to three decimal places. This is the margin of error.