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Angelina_Jolie [31]
3 years ago
5

The makers of a soft drink want to identify the average age of its consumers. A sample of 25 consumers was taken. The average ag

e in the sample was 31 years with a standard deviation of 3.8 years.The Margin of error of the 99% confidence interval for the average age of the consumers is a.1.90 years b.2.13 years c.4.10 years d.1.65 years
Mathematics
1 answer:
Lelu [443]3 years ago
8 0

Answer:

a.1.90 years

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.

In this question:

n = 25, \sigma = 3.8

So

M = 2.575*\frac{3.8}{\sqrt{25}} = 1.90

So the correct answer is:

a.1.90 years

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