Question

A study of two hundred teens found that the number of hours they spend on social networking sites each week is normally distributed with a mean of 12 hours. The population standard deviation is 4 hours. What is the margin of error for a 98% confidence interval?

0.122

0.659

0.295

0.313

Answer 1

@ganeshie8

Answer 2

The margin of error is given by:
\[z \times \frac{\sigma}{\sqrt{n}}\]
Do you know the value of z for a 98% confidence interval?

Answer 3

I have the table but don't know how to find the z value.?

Answer 4

It depends on the format of the table. Using my table I found the z value to be approximately 2.327. Now try using you table to find the cumulative probability for z = 2.327 and post the result.

Answer 5

@mathhelpnow Are you there?

Answer 6

Yes, just don't see 2.327 on my z-table. Outside, there are numbers on the outer left and top. Do I match up any numbers there?

Answer 7

In the left hand column for z, find 2.3. Then move across to the left until you find .4901. This should be in the column headed .03 (or possibly just 3). Do this make sense?

Answer 8

Does this make*

Answer 9

Sorry, I'm new to the z-table; these are the numbers next to 2.3:
2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916

Answer 10

We need to interpolate to find a z value for 0.49 (which is half of 0.98 or 98%). In any case, using my estimate for z, we can find the margin of error from:
\[2.327\times\frac{4}{\sqrt{200}}=you\ can\ calculate\]

Answer 11

Using your format of normal distribution table, you need to estimate the z value for .9900.

Answer 12

I appears that your table has negative values of z as well as positive values.

Answer 13

Ok, How do I estimate that? 0.313 because it would be under the 0.3 column?

Answer 14

In your table, a z value of 2.33 gives a cumulative probability of .9901. Does that make sense?

Answer 15

Yes,,, so I use .9901?

Answer 16

Looking at the answer choices, it appears that a z value of 2.33 can be used in the calculation.

Answer 17

So the margin of error is:
\[2.33\times\frac{4}{\sqrt{200}}=you\ can\ calculate\]

Answer 18

Does the square root 200 make it: 2.33 x 4 / 10 sqrt 2 ?

Answer 19

Yes:
\[\frac{2.33\times4}{10\times \sqrt{2}}\]

Answer 20

Okay.

9.32 / 14.14 = 0.659!

Answer 21

Correct. Good work!

Answer 22

yay, thanks for the help:)

Answer 23

You're welcome :)