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.

hey there!

if she's saving for six months, let's divide the total number we need for the trip by six, dividing it into the amount that needs to be saved for each month.

500 ÷ 6 =

she needs to save at least this amount each month, so we should use this symbol: ≥

let x be the amount she saves each month.

your final answer is x ≥

hope this !