Question

If all other quantities remain the same, how does the indicated change affect the minimum sample size requirement?

(a) Increase in the level of confidence
(b) Increase in the error tolerance
(c) Increase in the population standard deviation

Answer 1

Increasing the level of confidence and population standard deviation increases the minimum sample size requirement, while increasing the error tolerance decreases it.

Step-by-step explanation:

When all other quantities remain the same, the minimum sample size requirement is affected differently depending on which quantity is changed:

1. If the level of confidence is increased, the minimum sample size requirement will increase. This is because a higher level of confidence requires a narrower confidence interval, which can only be achieved with a larger sample size.
2. If the error tolerance is increased, the minimum sample size requirement will decrease. A larger error tolerance allows for a wider confidence interval, which can be achieved with a smaller sample size.
3. If the population standard deviation is increased, the minimum sample size requirement will increase. A larger standard deviation leads to a wider confidence interval, which requires a larger sample size to maintain the desired level of confidence.