Confidence Interval - Minimum Sample Size

Quiz
•
Mathematics
•
University
•
Hard
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15 questions
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1.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
How do you calculate the standard error of the mean?
SEM = σ / √n
SEM = n / σ
SEM = σ * n
SEM = σ + n
2.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
What is the formula for calculating the minimum sample size for estimating a population mean?
n = (Z^2 * σ^2) / E^2
n = (E^2 * Z) / σ^2
n = (Z * σ) / E
n = (σ^2 * E) / Z^2
3.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
What is the Z-value for a 95% confidence level?
1.64
1.96
2.58
1.75
4.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
What is the formula for calculating the minimum sample size for estimating a population proportion?
n = (Z^2 * p * (1-p)) / E^2
n = (Z * p) / E
n = (Z^2 * p) / (1-p)
n = (E^2 * p * (1-p)) / Z^2
5.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
What is the relationship between sample size and the precision of an estimate?
Larger sample sizes generally lead to more precise estimates, resulting in narrower confidence intervals and a higher likelihood of capturing the true population parameter.
Smaller sample sizes provide more precise estimates due to reduced variability.
Sample size has no effect on the precision of an estimate.
Larger sample sizes lead to less precise estimates because of increased variability.
6.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
If a researcher wants to estimate a proportion with a margin of error of 0.05 and a confidence level of 95%, what is the impact of increasing the margin of error on the required sample size?
Increasing the margin of error will decrease the required sample size, as a larger margin allows for a less precise estimate.
Increasing the margin of error will increase the required sample size, as a larger margin requires more precision.
Increasing the margin of error has no effect on the required sample size.
Increasing the margin of error will make the sample size irrelevant.
7.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
What is the margin of error in the context of confidence intervals?
The margin of error is the range within which the true population parameter is expected to lie, given a certain level of confidence. It is calculated as the product of the Z-value and the standard error.
The margin of error is the maximum amount that the sample results can differ from the true population parameter.
The margin of error is a statistical term that describes the likelihood that a sample accurately reflects the population.
The margin of error is the difference between the highest and lowest values in a data set.
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