1. Upcoming Schedule PSU Stat Jan 2015
Monday
Tuesday
Wednesday
Thursday
Friday
Jan 5
Sec 7.2
Jan 6
Jan 7
Jan 8
Sec 7.3
Jan 9
Jan 12
Sec 7.4
Jan 13
Sec7.4
Jan 14
Jan 15
Review
Jan 16
MLK Jr Day
No School
Jan 20
Chapter 7
test
Jan 21
Jan 22
Jan 23

2. Finals Schedule for First Semester: Monday the 26th is a Skinny day.
Tuesday the 27th is A-Day classes.
Wednesday the 28th is B-Day Finals.
Thursday the 29th is A-Day Finals.
Friday the 30th is the Planning Day.

3. Given CI=99%, give as much information as you can about the diagram below. Use proper symbols.
Bluman, Chapter 6

4. 95% Confidence Interval of the Mean
Bluman, Chapter 7

5. Confidence Interval of the Mean for a Specific z
90%
1.65
95%
1.96
98%
2.33
99%
2.58
Common confidence intervals, CI, and z scores associated with them.

6. 7.2 Confidence Intervals for the Mean When  Is Unknown
The value of , when it is not known, must be estimated by using s, the standard deviation of the sample.
When s is used, especially when the sample size is small (n<30), critical values greater than the values for
are used in confidence intervals in order to keep the interval at a given level, such as the 95%.
These values are taken from the Student t distribution, most often called the t distribution.
Bluman, Chapter 7

7. Characteristics of the t Distribution
The t distribution is similar to the standard normal distribution in these ways:
1. It is bell-shaped.
2. It is symmetric about the mean.
3. The mean, median, and mode are equal to 0 and are located at the center of the distribution.
4. The curve never touches the x axis.
Bluman, Chapter 7

8. Characteristics of the t Distribution
The t distribution differs from the standard normal distribution in the following ways:
1. The variance is greater than 1.
2. The t distribution is actually a family of curves based on the concept of degrees of freedom, which is related to sample size.
3. As the sample size increases, the t distribution approaches the standard normal distribution.
Bluman, Chapter 7

9. Degrees of Freedom
The symbol d.f. will be used for degrees of freedom.
The degrees of freedom for a confidence interval for the mean are found by subtracting 1 from the sample size. That is, d.f. = n - 1.
Note: For some statistical tests used later in this book, the degrees of freedom are not equal to n - 1.
Bluman, Chapter 7

10. Formula for a Specific Confidence Interval for the Mean When  Is Unknown and n < 30
The degrees of freedom are n - 1.
Bluman, Chapter 7

11. Chapter 7 Confidence Intervals and Sample Size
Section 7-2
Example 7-5
Page #371
Bluman, Chapter 7

12. Example 7-5: Using Table F
Find the tα/2 value for a 95% confidence interval when the sample size is 22.
Degrees of freedom are d.f. = 21.
Bluman, Chapter 7

13. Chapter 7 Confidence Intervals and Sample Size
Section 7-2
Example 7-6
Page #372
Bluman, Chapter 7

14. Example 7-6: Sleeping Time
Ten randomly selected people were asked how long they slept at night. The mean time was 7.1 hours, and the standard deviation was 0.78 hour. Find the 95% confidence interval of the mean time. Assume the variable is normally distributed.
Since  is unknown and s must replace it, the t distribution (Table F) must be used for the confidence interval. Hence, with 9 degrees of freedom, tα/2 =
Bluman, Chapter 7

15. Example 7-6: Sleeping Time
One can be 95% confident that the population mean is between 6.5 and 7.7 inches.
Bluman, Chapter 7

16. Chapter 7 Confidence Intervals and Sample Size
Section 7-2
Example 7-7
Page #372
Bluman, Chapter 7

17. Example 7-7: Home Fires by Candles
The data represent a sample of the number of home fires started by candles for the past several years. Find the 99% confidence interval for the mean number of home fires started by candles each year.
Step 1: Find the mean and standard deviation. The mean is = and standard deviation s =
Step 2: Find tα/2 in Table F. The confidence level is 99%, and the degrees of freedom d.f. = 6
t .005 =
Bluman, Chapter 7

18. Example 7-7: Home Fires by Candles
Step 3: Substitute in the formula.
One can be 99% confident that the population mean number of home fires started by candles each year is between and , based on a sample of home fires occurring over a period of 7 years.
Bluman, Chapter 7

19. Z or t; see page 373 Please read the paragraph on top of the page.
Bluman, Chapter 7

20. z or t, page 373 Is s known? No yes
Use ta/2 values and s in the formula
Use Za/2 values and s in the formula
Bluman, Chapter 7

21. Homework Sec 7.2 Page 374 #1-4 all and 5-19 every other odds
Optional: if you have a TI 83 or 84 calc see page 376
Bluman, Chapter 7