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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 - .

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Stat 100, This week

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  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”

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