1. Question: The population standard deviation for the number of corn kernels on an ear of corn is 94 kernels. If we want to be 90%confident that the sample mean is within 17 kernels of the true population mean, what is the minimum sample size that should be taken?
2. Question: Suppose the scores ...
Week 6 Assignment: Confidence Interval for Mean – Population Standard
Deviation Known
Find the sample size required to estimate a population mean with a given confidence level
Question
The population standard deviation for the number of corn kernels on an ear of corn
is 94 kernels. If we want to be 90%confident that the sample mean is
within 17 kernels of the true population mean, what is the minimum sample size
that should be taken?
z0.101.282 z0.051.645 z0.0251.960. z0.012.326. z0.0052.576
Use the table above for the z-score.
n=z2σ2EBM2
In this formula,
z=zα2=z0.05=1.645
because the confidence level is 90%. From the problem, we know
that σ=94 and EBM=17. Therefore,
n=z2σ2EBM2=(1.645)2(94)2172≈82.74
Use n=83 to ensure that the sample size is large enough.
Find the sample size required to estimate a population mean with a given confidence level
Question
Suppose the scores of a standardized test are normally distributed. If the
population standard deviation is 2 points, what minimum sample size is needed to
be 90% confident that the sample mean is within 1 point of the true population
mean?
z0.101.282z0.051.645z0.0251.960z0.012.326z0.0052.576
, Use the table above for the z-score, and be sure to round up to the nearest integer.
Yes that's right. Keep it up!
11 test scores
Answer Explanation
Correct answers:
11 test scores
The formula for sample size is
n=z2σ2EBM2
In this formula,
z=zα2=z0.05=1.645
because the confidence level is 90%. From the problem, we know
that σ=2 and EBM=1. Therefore,
n=z2σ2EBM2=(1.645)2(2)212≈10.82
Use n=11 to ensure that the sample size is large enough.
Also, the sample size formula shown above is sometimes written using an alternate
format of n=(zσE)2. In this formula, E is used to denote margin of error and the
entire parentheses is raised to the exponent 2.
Therefore, the margin of error for the mean can be denoted by "EBM" or by "E".
Either formula for the sample size can be used and these formulas are considered
as equivalent.
Calculate and interpret the confidence interval for a population mean with a known standard deviation
Question
The length, in words, of the essays written for a contest are normally distributed
with a population standard deviation of 442 words and an unknown population
mean. If a random sample of 24 essays is taken and results in a sample mean
of 1330 words, find a 99% confidence interval for the population mean.
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