Five hundred randomly selected adult residents in Sacramento are surveyed to determine whether they believe children should have limited smartphone access. Of the 500 people surveyed, 381 responded yes - they believe children should have limited smartphone access. You wish to estimate a population mean y with a known population standard devi- ation o = 3.5. If you want the error bound E of a 95% confidence interval to be less than 0.001, how large must the sample size n be?

The sample size must be of 47,059,600.

Step-by-step explanation:

We have to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Z-table as such z has a p-value of .

That is z with a p-value of , so Z = 1.96.

Now, find the margin of error M as such

In which is the standard deviation of the population and n is the size of the sample.

Standard deviation:

If you want the error bound E of a 95% confidence interval to be less than 0.001, how large must the sample size n be?

This is n for which M = 0.001. So

The sample size must be of 47,059,600.

question:

could we have options?

7

step-by-step explanation: