A population has standard deviation σ =17.5. Required:
a. How large a sample must be drawn so that a 99.9% confidence interval for will have a margin of error equal to 4.1. Round the critical value to no less than three decimal places. Round the sample size up to the nearest integer. A sample size of is needed to be drawn in order to obtain a confidence interval with a margin of error equal to 4.1 .

b. If the required confidence level were 95%, would the necessary sample size be larger or smaller?

a) A sample size of 195 is needed.

b) Smaller

Step-by-step explanation:

We have that 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 Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

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.

a. How large a sample must be drawn so that a 99.9% confidence interval for will have a margin of error equal to 4.1.

We need a sample size of n.

n is found when

We have that

So

Rounding up

A sample size of 195 is needed.

b. If the required confidence level were 95%, would the necessary sample size be larger or smaller?

Same as above for n, the difference is that z would be 1.96 instead of 3.27. So a smaller sample size.

these sign is used to tell weather the number is greater or less than the number   <   or >     but this sign means its equal =    

hope this you and

step-by-step explanation: