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pishuonlain [190]
3 years ago
9

The number of hours that a nine month old baby sleeps at night are normally distributed with a population standard deviation of

1.5 hours and an unknown population mean. A random sample of 22 nine month old babies is taken and results in a sample mean of 12 hours. Find the margin of error for a confidence interval for the population mean with a 90% confidence level.
Mathematics
1 answer:
natita [175]3 years ago
3 0

Answer:

The margin of error is of 0.7123 hours.

Step-by-step explanation:

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

\alpha = \frac{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*\frac{\sigma}{\sqrt{n}}

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

Find the margin of error for a confidence interval for the population mean with a 90% confidence level.

We have that \sigma = 1.5, n = 12. So

M = 1.645*\frac{1.5}{\sqrt{12}} = 0.7123

The margin of error is of 0.7123 hours.

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