1. Confidence Intervals of the Mean 2 nd part of ‘estimate of the mean’ presentation

2. Mu is between the two values calculated by:

3. Always draw the N.D. The shaded area can help us to see what we mean by It is the border of the shaded area to the right of the mean. We are saying that the mean lies between that border and the corresponding left-side border

4. Write the equation Mu lies between the two values within the parentheses

5. Practical Statement of Result With 95% confidence, we can say that u will be ≤ 1.96 *S.E. and ≥ -1.96 * S.E. We call 1.96 the reliability coefficient

6. The Math X = 22, n = 10, б 2 = 45 Review what the symbols mean? Find the quantity б = Γ45 = 6.7 б / Γn = 6.7/ Γ10 = 6.7 / 3.16 = 2.12 1.96 * 2.12 = 4.16 Mu is between 22 – 4.16 and 22 + 4.16 17.84 ≤ µ ≤ 26.16 with 95% confidence Z * б / Γn

7. ‘Significance Level’ Related to confidence interval 95% confidence level can be expressed as 0.05 significance level Alpha is term for significance level

8. Another Example Page 230, #13 Take out diskette from back of book Insert into computer Click on Install Check ASCII, excel, SPSS Install to hard drive

9. Excel Go to “exercise” Find “lowbwt” Save to hard drive to work on File will probably be gone next time you return. Save the data set we want onto your own floppy

10. Do Problem 13, just the males

11. Separate male & female, how?

12. Important Statements in the Problem 1.Large sample

13. Applications If we know a population mean & st. dev., we can calculate the probability that any sample will have a stated mean. A certain large human pop’n has a cranial length that is approx’ly normally distributed with mean 185.6 mm and б of 12.7 mm.

14. µ = 185.6 mm б = 12.7 mm What is the probability that a random sample of size 10 from this population will have a mean greater than 190? We can calculate this probability but why would we?

15. Usefulness?? Let’s say that it is accepted knowledge that the population has a certain mean. I am working with a group of people. I want to know if they fit into this population with regard to the particular parameter. If the probability of the mean of the sample is very low, perhaps it is not really from the same population

16. Education Example Third-graders in the U.S. have an average reading score of 124. Third-graders in a particular school have a mean reading score of 120. What’s the probability that they are from the same population?

17. Back to Cranial Length µ = 185.6 mm б = 12.7 mm random sample of size 10 from this population will have a mean greater than 190? Have to find how far 190 is from 185.6 in units of standard error of the mean

18. Probability of Mean of 190 Did you draw a normal dist??? Z = 4.4 / 12.7 / 3.16 Z = 1.09 Area = 0.138 The probability is 13.8% 185.6 190 01.09 0.138

19. The mean & st. dev. of serum iron values are 120 & 15 micrograms per 100 ml. What is the probability that a random sample of 50 normal men will yield a mean between 115 & 125 µg/100ml? µ = 120 б = 15 Z 1 = (115-120) / 15 / sqrt of 50 Z 2 = (125-120) / 15 / sqrt of 50

20. Z 1 = (115-120) / 15 / sqrt of 50 Z 2 = (125-120) / 15 / sqrt of 50 Draw the Normal Distribution