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Yuri [45]
3 years ago
7

A corporation with several thousand employees wants to estimate the mean commute time for all employees. They would like to cons

truct a 95% confidence interval with a margin of error of no more than 4 minutes. Preliminary interviews with a small sample suggest that a reasonable estimate of the population standard deviation is σ = 10 minutes. Which of the following is the smallest sample the company can take to achieve the desired margin or error?
A.5
B.24
C.25
D.41
E.42
Mathematics
1 answer:
velikii [3]3 years ago
3 0

Answer:

C.25

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{1-0.95}{2} = 0.025

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 1-0.025 = 0.975, so z = 1.96

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.

Which of the following is the smallest sample the company can take to achieve the desired margin or error?

This is n when \sigma = 10, M = 4

M = z*\frac{\sigma}{\sqrt{n}}

4 = 1.96*\frac{10}{\sqrt{n}}

4\sqrt{n} = 1.96*10

\sqrt{n} = \frac{1.96*10}{4}

(\sqrt{n})^{2} = (\frac{1.96*10}{4})^{2}

n = 24.01

We have to round up.

So the correct answer is:

C.25

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we know that

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we have

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simplify

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Step-by-step explanation:

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------------- x   -----------

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Step 2: Multiply the numerators and the denominators.

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------------------------------------------

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Now let's simplify to get the answer.

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-----------------------------

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= √30 -3√2 +√55                                     [√18 = √9√2 = 3√2]

--------------------------

2      

The answer is  \sqrt{30}  - 3 \sqrt{2}  +  \sqrt{55}  -  \sqrt{33}  \div 2


Thank you.

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