Download 8.1 Confidence Intervals about a Population Mean

8.1 Confidence Intervals about a Population Mean ­ known population standard deviation.
Parent Population
mean:
standard deviation:
Sampling Distribution
mean:
standard deviation:
Formulas to:
find the Z­Score from an observation
find an observation from the Z­score
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8.1 Confidence Intervals about a Population Mean ­ known population standard deviation.
8.1 Confidence Intervals about a Population Mean
We are going to be using information about a random sample chosen from a population to estimate information about the population. Today we're going to be estimating the population mean μ.
Vocabulary:
90%
Meaning of a confidence interval: a 90% confidence interval with a lower bound of 12 and an upper bound of 18 would mean:
"We are 90% confident that μ is between 12 and 18"
Notations and formulas:
Confidence interval
has an area of Area of the tails
Boundaries of the confidence interval Margin of Error: how far from the actual mean could our estimate be.
"We are 90% confident that μ is between 12 and 18"
We think the mean is The margin of error is
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8.1 Confidence Intervals about a Population Mean ­ known population standard deviation.
A simple random sample of size n is selected from a population with σ = 3.8 The mean of the sample is calculated and is 59.2.
What is the point estimate for the mean?
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8.1 Confidence Intervals about a Population Mean ­ known population standard deviation.
Determining the sample size, n, needed to estimate μ with a specific level of confidence and a specific margin of error, E, is given by
A doctor wants to estimate the mean serum HDL cholesterol of 20 ­ 29 year old men. How many subjects would be needed in a sample in order to estimate the mean serum HDL levels with 90% certainty that μ is within 1.5 points of our estimate. Assume σ = 12.5.
Suppose the doctor would prefer 98% confidence. What sample size would be necessary?
How does increasing the confidence level affect the sample size needed?
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8.1 Confidence Intervals about a Population Mean ­ known population standard deviation.
Which are normal? Why or why not?
A researcher is interested in approximating the mean number of miles that 3­year old Chevy Cavaliers have been driven. She randomly selects 35 Cavaliers in the Orlando, Florida area and obtains the odometer readings in the table. Construct and interpret a 95% confidence interval for the mean. Assume σ = 16,100 HW: p466 C&V #3 ­ 6, p466 #1 ­ 11odd, 19, 25, 27
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