Please forgive me for posting this for the 3rd time but I really need to learn this:

A researcher conducted a study of the access speed of 45 hard drives and concluded that his maximum error of estimate was 28. If he were to conduct a second study to reduce the maximum error of estimate to 7, about how many hard drives should he include in his new sample?
Select one:
a. 720
b. 45
c. 90
d. 180
Please can someone explain me how to do the above problem.
My working: 28/7 = 4, so 4^2=16
16 x 45 =720.
I am not sure if the above working is correct but please i really need help in learning this problem (question). So, Please can anyone assist me by showing the correct method for this.
Thanks.

To answer this question, you need to understand the concept of sample size and maximum error of estimate.

Maximum error of estimate is a measure of how much the sample mean is expected to deviate from the true population mean. It is usually denoted as 'E' or 'ME' in formulas. In this case, the researcher wants to reduce the maximum error of estimate to 7.

The formula to calculate the maximum error of estimate is:

ME = Z * (standard deviation / √n)

Where:
ME is the maximum error of estimate
Z is the z-score corresponding to the desired confidence level
Standard deviation is the population standard deviation (or an estimate, if it's not known)
n is the sample size

In this case, since we don't have the population standard deviation, we can use the maximum error of estimate from the first study (28) as an estimate for the standard deviation.

From your working, you correctly calculated the ratio between the two maximum errors of estimate (28/7 = 4). However, you squared that ratio (4^2 = 16), which is not accurate. Instead, you need to square the ratio of the sample sizes:

Sample size ratio = (new maximum error of estimate / current maximum error of estimate)^2

Using this formula, the sample size ratio would be (7/28)^2 = 1/16.

To find the new sample size, multiply the current sample size by the sample size ratio:

New sample size = current sample size * sample size ratio

Plugging in the current sample size of 45:

New sample size = 45 * (1/16) = 2.81

Since you cannot have a fraction of a hard drive, you would round up the new sample size to the nearest whole number. Therefore, the researcher should include about 3 hard drives in the new sample.

Given the answer choices, none of them is correct because they are all whole numbers. It seems there could be an error in the answer choices provided.