1. You want to estimate the population of

Berlecia Howe

Berlecia Howe

Answered question

2022-10-06

1. You want to estimate the population of waiting times for hospital emergency rooms. You want to be 99% confident that the sample standard deviation is within 1% of the population standard deviation. Find the minimum sample size.

Answer & Explanation

Don Sumner

Don Sumner

Skilled2023-05-29Added 184 answers

To find the minimum sample size needed to estimate the population of waiting times for hospital emergency rooms with a 99% confidence level and an acceptable error margin of 1% for the sample standard deviation compared to the population standard deviation, we can use the formula for minimum sample size:
n=(Z·σE)2
where:
n represents the sample size,
Z is the z-score corresponding to the desired confidence level,
σ is the population standard deviation, and
E is the acceptable error margin for the sample standard deviation.
In this case, we want to be 99% confident, which means the z-score corresponding to a 99% confidence level is approximately 2.576 (from the standard normal distribution table).
We can represent the formula and values as follows:
n=(2.576·σ0.01·σ)2
Simplifying the equation, we get:
n=(2.5760.01)2
n=657.69
Rounding up to the nearest whole number, the minimum sample size needed is n=658.
Therefore, a minimum sample size of 658 is required to estimate the population of waiting times for hospital emergency rooms with a 99% confidence level and an acceptable error margin of 1% for the sample standard deviation compared to the population standard deviation.

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