A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spent studying per week. Assuming a population standard deviation of three hours, what is the required sample size if the error should be less than a half hour with a 99% level of confidence? Select one: a. 196 b. 239 c. 15 d. 16

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joaobezerra joaobezerra · Answer 1 · 2020-01-11T04:48:34+01:00

Answer:

b. 239

Step-by-step explanation:

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

[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.05 = 0.995[/tex], so [tex]z = 2.575[/tex]

Now, find M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

In this problem, we have that:

[tex]M = 0.5, \sigma = 3[/tex]

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.5 = 2.575*\frac{3}{\sqrt{n}}[/tex]

[tex]0.5\sqrt{n} = 7.725[/tex]

[tex]\sqrt{n} = 15.45[/tex]

[tex]n = 238.7[/tex]

So a sample of at least 239 is required.

The correct answer is:

b. 239