197k views
1 vote
The makers of a soft drink want to identify the average age of its consumers. A sample of 25 consumers was taken. The average age 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

User Karlth
by
8.2k points

1 Answer

5 votes

Answer:

a.1.90 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 = (1-0.99)/(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*(\sigma)/(√(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*(3.8)/(√(25)) = 1.90

So the correct answer is:

a.1.90 years

User Martin Sherburn
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories