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A group of 49 randomly selected students has a mean age of 22.4 years with a standarddeviation of 3.8. Construct a 98% confidence interval for the population mean knowing thatthe population standard deviation is 4.2 years.

User Anupam Srivastava
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1 Answer

28 votes
28 votes

Answer:

The 98% confidence interval for the population mean is between 21 and 23.8 years.

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 - 0.98)/(2) = 0.01

Now, we have to find z in the Z-table as such z has a p-value of
1 - \alpha.

That is z with a pvalue of
1 - 0.01 = 0.99, so Z = 2.327.

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 = 2.327(4.2)/(√(49)) = 1.4

The lower end of the interval is the sample mean subtracted by M. So it is 22.4 - 1.4 = 21 years.

The upper end of the interval is the sample mean added to M. So it is 22.4 + 1.4 = 23.8 years.

The 98% confidence interval for the population mean is between 21 and 23.8 years.

User Gopal S Akshintala
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