1. Confidence Interval for a Population mean ( known)
(Z-Interval)
estimate  margin of error
estimate  critical value  standard error 

2. Properties of Confidence Intervals
The interval is always centered around the statistic
The higher the confidence level, the wider the interval becomes
If you increase n, then the margin of error decreases

3. Stat – Tests – ZInterval
Calculator Tip:
Z-Interval
Stat – Tests – ZInterval
Data: If given actual values
Stats: If given summary of values

4. Conditions for a Z-Interval:
SRS
(should say)
(CLT or population approx normal)
2. Normality
(Population 10x sample size)
3. Independence

5. Example #1
Serum Cholesterol-Dr. Paul Oswick wants to estimate the true mean serum HDL cholesterol for all of his year old female patients. He randomly selects 30 patients and computes the sample mean to be Assume from past records, the population standard deviation for the serum HDL cholesterol for year old female patients is =13.4.
Construct a 95% confidence interval for the mean serum HDL cholesterol for all of Dr. Oswick’s year old female patients.
Parameter:
The true mean serum HDL cholesterol for all of Dr. Oswick’s year old female patients.

6. Check conditions:
SRS:
Says randomly selected
Normality:
Approximately normal by the
CLT (n  30)
Independence:
I am assuming that Dr. Oswick has 300 patients or more.
What you are calculating:
One sample Z-Interval

7. Calculate:
Interpret:

8. 53 is contained in the interval.
Example #1
Serum Cholesterol-Dr. Paul Oswick wants to estimate the true mean serum HDL cholesterol for all of his year old female patients. He randomly selects 30 patients and computes the sample mean to be Assume from past records, the population standard deviation for the serum HDL cholesterol for year old female patients is =13.4.
b. If the US National Center for Health Statistics reports the mean serum HDL cholesterol for females between years old to be  = 53, do Dr. Oswick’s patients appear to have a different serum level compared to the general population? Explain.
No,
53 is contained in the interval.

9. Lower confidence level
Example #1
Serum Cholesterol-Dr. Paul Oswick wants to estimate the true mean serum HDL cholesterol for all of his year old female patients. He randomly selects 30 patients and computes the sample mean to be Assume from past records, the population standard deviation for the serum HDL cholesterol for year old female patients is =13.4.
c. What two things could you do to decrease your margin of error?
Increase n
Lower confidence level

10. The true mean weight of Snickers 1-oz Fun-size candy bars
Example #2
Suppose your class is investigating the weights of Snickers 1-ounce Fun-Size candy bars to see if customers are getting full value for their money. Assume that the weights are Normally distributed with standard deviation = 0.05 ounces. Several candy bars are randomly selected and weighed with sensitive balances borrowed from the physics lab. The weights are
ounces. Determine a 90% confidence interval for the true mean, µ. Can you say that the bars weigh 1oz on average?
Parameter:
The true mean weight of Snickers 1-oz Fun-size candy bars

11. Check conditions:
SRS:
Says randomly selected
Normality:
Approximately normal because the population is approximately normal
Independence:
I am assuming that Snickers
has 80 bars or more in the 1-oz size
What you are calculating:
One sample Z-Interval

12. Calculate:

13. Interpret:
I am 90% confident the interval .966 to ounces captures the true mean weight of Snickers 1-oz Fun-size candy bars.
Since 1 ounce is in our interval, we can say that the average is around 1 ounce with 90% confidence.

14. What is the sample mean income?
Example #3
A statistician calculates a 95% confidence interval for the mean income of the depositors at Bank of America, located in a poverty stricken area. The confidence interval is $18,201 to $21,799.
What is the sample mean income?

15. b. What is the margin of error?
Example #3
A statistician calculates a 95% confidence interval for the mean income of the depositors at Bank of America, located in a poverty stricken area. The confidence interval is $18,201 to $21,799.
b. What is the margin of error? m
m = 21,799 – 20,000
m = 1,799

16. Choosing a Sample Size for a specific margin of error
Note: Always round up! You can’t have part of a person! Ex: rounds up to 164.

17. Example #4
A researcher wishes to estimate the mean number of miles on four-year-old Honda Accords. How many cars should be in a sample in order to estimate the mean number of miles within a margin of error of  1000 miles with 99% confidence assuming =19,700.