1 / 17

Stat 100, This week

Stat 100, This week. Chapter 20, Try Problems 1-9 Read Chapters 3 and 4 (Wednesday’s lecture). Confidence level. Probability that procedure provides interval that captures the population value Most commonly used level is 95% confidence Other confidence levels are possible. For Ch. 19 -.

kaden
Download Presentation

Stat 100, This week

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Stat 100, This week • Chapter 20, Try Problems 1-9 • Read Chapters 3 and 4 (Wednesday’s lecture)

  2. Confidence level • Probability that procedure provides interval that captures the population value • Most commonly used level is 95% confidence • Other confidence levels are possible

  3. For Ch. 19 - • Margin of error for 95% confidence is

  4. For other confidence levels .. • Change the number “2” in the formula • Chart on page 345 of book shows other values • For example, for 99.7% confidence use “3” instead of “2”

  5. For 99.7% confidence • Margin of error =

  6. Example • In a Stat 200 survey of n = 200 students, 65% said they believe there is extraterrestrial life • p= .65, n = 200 • For 99.7% CI, margin of error = • 3 sqrt [.65(1-.65)/200] = 3.034 = .102 • 99.7% CI is 65%  10%, or 55% to 75%

  7. Elements of problem • Population = all college students • Sample = 200 Stat 200 students • Sample value = 65% believe there is ET • Population value= We’re 99.7% sure that it’s between 55% and 75%

  8. Chapter 19 Thought Question 1 • Study of n = 199 British married couples gives 95% CI as .02 to .08 for proportion of couples in which wife is taller that husband. • Interpret this interval. • We can be 95% sure that wife is taller than husband in somewhere between .02 and .08 of all British married couples (not just the 199 studied)

  9. Chapter 19 Thought Question 2 • Do you think a 99% confidence interval for Question 1 would be wider or narrower than the 95% interval? • Answer = wider. We would be more sure that the interval would catch true population value with a wider interval

  10. Chapter 19 Thought Question 3 • Poll result is given that a 95% CI for percent believing in faith healing in U.S. is 42% to 48%. • Poll had n =1000 • Suppose the sample size had been n = 5000. Would the 95% CI have been wider or narrower? • Answer = narrower. With larger n, the margin of error is smaller so the interval is narrower.

  11. Chapter 20 Thought Question 1 • Study compares weight loss of men who only diet compared to those who only exercise • 95% confidence intervals for mean weight loss • Diet only : 13.4 to 18.0 • Exercise only 6.4 to 11.2

  12. Part a. • Do you think this means that 95% of men who diet will lose between 13.4 and 18.0 pounds? • Answer = NO. A confidence interval does not estimate individual values.

  13. Part b. • Can we conclude that there's a difference between mean weight losses of the two programs? • This is a reasonable conclusion. The two confidence intervals don't overlap.

  14. Thought Question 2 • Suppose the sample sizes had been larger than they were for question 1. • How would that change the confidence intervals? • Answer = with larger sample size margin of error is smaller so confidence interval is narrower

  15. Thought Question 3 of Ch. 20 • We compared confidence intervals for mean weight loss of the two different treatments. • What would be a more direct way to compare the weight losses in question 1? • Answer = get a single confidence interval for the difference between the two means. • This is possible, but we won’t go over the details

  16. Thought Question 4 • A study compares risk of heart attack for bald men to risk for men with no hair loss • A 95% confidence interval for relative risk is 1.1 to 8.2 • Is it reasonable to conclude that bald men generally have a greater risk?

  17. Answer • Relative risk = risk in group 1/ risk in group 2 • Relative Risk =1 if risks are equal • Interval 1.1 to 8.2 is completely above 1 so it seems that the “true” relative risk may be greater than 1. • So bald men may have a higher risk – but note we have very imprecise estimate of “how much”

More Related