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Unformatted text preview: grams—determine interval estimate
Standard deviation σ = 15 grams Sampling distribution for Sample Size n = 25:
◦ Normal distribution (population follows normal distribution): Interval Estimation Sample mean = 362.3 grams (given in problem)
Standard error of the mean: σ =σ =
3
x
2
5 Confidence Interval
◦ . 3.
9
8
margin of error is 5.88: z σ z531 ⋅ = 8
α x=02 = 6 5
2
0
. ◦ therefore, interval is ◦ 3 23 58
6. ± . 8
Interval Estimate
3 64 ≤µ 3 81
5. 2 ≤ 6. 8
Given a sample mean of 362.3, we can be 95% confident that the
population mean is between 356.42 and 368.18 grams. Using MS Excel Interval Estimation =CONFIDENCE.NORM(alpha,standard_dev,size) Returns the margin of error that you can use to
construct a confidence interval for a population
mean. The confidence interval is a range of values.
Your sample mean, x, is at the center of this range
and the range is x ± CONFIDENCE.NORM
Note: alpha—level of significance standard_dev—standard deviation of population
(not standard error of the mean) size—sample size Using MS Excel Interval Estimation =CONFIDENCE.NORM(alpha,standard_dev,size) Returns the margin of error that you can use to
construct a confidence interval for a population
mean. The confidence interval is a range of values.
Your sample mean, x, is at the center of this range
and the range is x ± CONFIDENCE.NORM
Note: alpha—level of significance
SAFETY CHECK:
CONFIDENCE.NORM can standard_dev—standard deviation of population
only
(not standard error of the mean) be used for finding the
margin of error for a population size—sample size
mean when the standard
deviation is known. σ Known Example
If the sample mean is found to be 362.3, find the 95%
confidence interval (i.e., interval estimate) for the population
mean. Population distribution:
◦ Normal distribution: Mean μ = ? grams—determine interval estimate
Standard deviation σ = 15 grams Sampling distribution for Sample Size n = 25:
◦ Normal distribution (population follow...
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 Spring '13

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