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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
Stat 100, This week
  • Chapter 20, Try Problems 1-9
  • Read Chapters 3 and 4 (Wednesday’s lecture)
confidence level
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
For Ch. 19 -
  • Margin of error for 95% confidence is
for other confidence levels
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”
for 99 7 confidence
For 99.7% confidence
  • Margin of error =
example
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%
elements of problem
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%
chapter 19 thought question 1
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)
chapter 19 thought question 2
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
chapter 19 thought question 3
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.
chapter 20 thought question 1
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
part a
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.
part b
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.
thought question 2
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
thought question 3 of ch 20
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
thought question 4
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?
answer
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”