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.
Thanks!
To determine how many hard drives the researcher should include in the new sample to reduce the maximum error of estimate to 7, we can use the formula for the sample size calculation:
n = (Z * σ / E) ^ 2
Where:
n = sample size
Z = Z-score corresponding to the desired level of confidence (e.g., 1.96 for a 95% confidence level)
σ = standard deviation (or maximum error of estimate) from the first study
E = desired maximum error of estimate for the second study
In this case, the researcher conducted the first study and found that the maximum error of estimate (σ) was 28. The desired maximum error of estimate for the second study (E) is 7.
Plugging these values into the formula, we have:
n = (1.96 * 28 / 7) ^ 2
n = (1.96 * 4) ^ 2
n = 7.84 ^ 2
n ≈ 61.4656
Since the sample size must be a whole number, we round up to the nearest whole number to ensure an adequate sample size. Therefore, the researcher should include approximately 62 hard drives in the new sample.
Note: It is worth mentioning that the available answer choices do not include 62, so none of the given options are correct.