A researcher conducted a study of the access speed of 40 hard drives and concluded that his
maximum error of estimate was 15. If he were to conduct a second study to reduce the
maximum error of estimate to 5, about how many hard drives should he include in his new
sample?
SEm = SD/√n
15 = SD/√40 (Calculate SD and insert below.)
5 = SD/√?
A researcher conducted a study of the access speed of 35 hard drives and concluded that his maximum error of estimate was 35. 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?
To determine the number of hard drives the researcher should include in the new sample to reduce the maximum error of estimate to 5, we need to use a formula called the sample size formula.
The sample size formula is given by:
n = (Z * σ / E)^2
where:
n = sample size
Z = z-score, representing the desired level of confidence (typically based on a standard normal distribution, such as 1.96 for a 95% confidence level)
σ = standard deviation of the population
E = maximum error of estimate
In this case, the researcher wants to reduce the maximum error of estimate from 15 to 5. Therefore, E = 5.
However, the problem statement does not provide the standard deviation of the population (σ). Without this information, we cannot directly calculate the required sample size.
If the researcher conducted the previous study and knows the sample standard deviation (s), they can use it as an estimate of the population standard deviation.
Based on the previous sample, if the researcher had calculated the sample standard deviation (s), they could use it as an estimate for σ. If s is available, the formula becomes:
n = (Z * s / E)^2
For example, if the researcher used a 95% confidence level (Z = 1.96) and estimated the population standard deviation as s = 15 from the previous study, they could calculate the new sample size using:
n = (1.96 * 15 / 5)^2
n = (29.4)^2
n ≈ 862.56
Therefore, the researcher should include approximately 863 hard drives in the new sample if they want to reduce the maximum error of estimate to 5, assuming a population standard deviation estimate of 15 from the previous study.