The national average for the number of students per teacher for all U.S. public schools in 15.9 Arandom sample of 12 school districts from a moderately populated area showed that the mean number of students per teacher was 19.2 with a variance of 4.41.  Estimate the true mean number of students per teacher with 95% confidence.  How does your estimate compare with the national average?

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Asked Jul 29, 2019
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The national average for the number of students per teacher for all U.S. public schools in 15.9 Arandom sample of 12 school districts from a moderately populated area showed that the mean number of students per teacher was 19.2 with a variance of 4.41.  Estimate the true mean number of students per teacher with 95% confidence.  How does your estimate compare with the national average?

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Expert Answer

Step 1

Confidence interval:

The (1-α) % confidence interval for population mean µ, when σ is unknown is given by:

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Step 2

Computing the confidence interval for population mean:

A random sample of 12 school districts from a moderately populated area shows that the mean number of students per teachers is 19.2 with variance 4.41. That is, n=12, x-bar = 19.2 and s2 = 4.41.The confidence level is 95%. Therefore, the significance level, α = 0.05.

From the EXCEL, using the formula, =T.INV.2T(0.05,11), the critical value is 2.20.

Therefore the 95% confidence interval of the mean when the standard deviation is unknown is,

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- 19.2 t 2.20 v4.41 V12 (19.2 1.3337) =(17.8663,20.5337)

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Step 3

The national average for the number of students per teachers for all U.S public schools is 15.9. But the 95% confidence interval for the true mean number o...

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