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serg [7]
3 years ago
15

You measure 34 backpacks' weights, and find they have a mean weight of 33 ounces. Assume the population standard deviation is 10

.9 ounces. Based on this, what is the maximal margin of error associated with a 99% confidence interval for the true population mean backpack weight
Mathematics
1 answer:
Dmitriy789 [7]3 years ago
6 0

Answer:

The maximal margin of error associated with a 99% confidence interval for the true population mean backpack weight is 4.81 ounces

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{1-0.99}{2} = 0.005

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 1-0.005 = 0.995, so z = 2.575

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.

So

M = 2.575*\frac{10.9}{\sqrt{34}} = 4.81

The maximal margin of error associated with a 99% confidence interval for the true population mean backpack weight is 4.81 ounces

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