1. Estimating a Population Mean
Warmup
You work for a consumer advocate agency and want to find the mean repair cost of a washing machine. As part of your study, you randomly select 40 repair costs and find the mean to be $ From past studies, you assume that the σ is $17.50.
Construct a 90% confidence interval. (Include all four steps: state the problem, check conditions, calculate the CI, and interpret it).
Estimating a Population Mean

2. Section 8.3 Estimating a Population Mean
Learning Objectives
After this section, you should be able to…
CONSTRUCT and INTERPRET a confidence interval for a population mean
DETERMINE the sample size required to obtain a level C confidence interval for a population mean with a specified margin of error
DESCRIBE how the margin of error of a confidence interval changes with the sample size and the level of confidence C
DETERMINE sample statistics from a confidence interval

3. Estimating a Population Mean
The One-Sample z Interval for a Population Mean
To calculate a confidence interval for µ , we use the familiar formula:
estimate ± (critical value) • (standard deviation of statistic)
Estimating a Population Mean
Choose an SRS of size n from a population having unknown mean µ and known standard deviation σ. As long as the Normal and Independent conditions are met, a level C confidence interval for µ is
The critical value z* is found from the standard Normal distribution.
One-Sample z Interval for a Population Mean

4. Estimating a Population Mean
Example #1
Researchers would like to estimate the mean cholesterol level µ of a particular variety of monkey that is often used in laboratory experiments. The standard deviation of cholesterol level is 5 mg/dl. A random sample of 40 monkeys was used and the sample mean was 53 mg/dl. Construct a 98% confidence interval for the mean cholesterol level of this type of monkey.
Estimating a Population Mean

5. Estimating a Population Mean
Example #2
Assume that systolic blood pressure (SBP) for healthy adults is normally distributed with σ = 20 mm Hg. If an SRS of 20 adults is selected and the mean of the sample is 118 mm HG, construct a 99% confidence interval for the mean systolic blood pressure of all adults.
Estimating a Population Mean

6. Estimating a Population Mean
Choosing the Sample Size
The margin of error ME of the confidence interval for the population mean µ is
Estimating a Population Mean
We determine a sample size for a desired margin of error when estimating a mean in much the same way we did when estimating a proportion.
Choosing Sample Size for a Desired Margin of Error When Estimating µ
To determine the sample size n that will yield a level C confidence interval for a population mean with a specified margin of error ME:
• • Set the expression for the margin of error to be less than or equal to ME and solve for n:

7. Estimating a Population Mean
Example: How Many Monkeys?
Researchers would like to estimate the mean cholesterol level µ of a particular variety of monkey that is often used in laboratory experiments. They would like their estimate to be within 1 milligram per deciliter (mg/dl) of the true value of µ at a 95% confidence level. A previous study involving this variety of monkey suggests that the standard deviation of cholesterol level is about 5 mg/dl.
Estimating a Population Mean

8. Estimating a Population Mean
Example: Blood Pressure
Assume that systolic blood pressure (SBP) for healthy adults is normally distributed with σ = 20 mm Hg. What sample size is needed so that 95% of sample means are between 116 mmHg and 124 mmHg?
Estimating a Population Mean