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A study of six hundred adults found that the number of hours they spend on social networking sites each week is normally distributed with a mean of 17 hours. The population standard deviation is 6 hours. What is the margin of error for a 95% confidence interval?

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merlynthewhizz
Margin of error = Critical Value × Standard Error

We work out critical value from the information of confidence interval. 
We have 95% confidence interval, hence the z-score (that is the critical value) is 1.96 (refer to the picture below)

Standard Error = [tex] \frac{standard deviation}{ \sqrt{sample size} } [/tex]
Standard Error = [tex] \frac{6}{ \sqrt{17} } =1.46[/tex]

Margin of error = 1.96 × 1.46 = 2.87 (rounded to 2 decimal place)
Ver imagen merlynthewhizz

Answer: The margin of error for a 95% confidence interval is 0.48.

Step-by-step explanation:

Since we have given that

N = 600

Mean = 17 hours

Standard deviation = 6 hours

We need to find the margin of error for a 95% confidence interval.

Margin of error is given by

[tex]Error=z\times \dfrac{\sigma}{\sqrt{n}}[/tex]

Here, n = 600, [tex]\sigma=6[/tex]

In 95% confidence interval z = 1.96

So, Margin of error would be

[tex]1.96\times \dfrac{6}{\sqrt{600}}\\\\=0.48[/tex]

Hence, the margin of error for a 95% confidence interval is 0.48.

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