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Confidence Interval

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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 • Margin of error for 95% confidence is

p(1  p) 2 n

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
p(1  p) • Margin of error = 3 n

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
• • • • 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
• 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
• 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
• 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
• 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.
• 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.
• 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
• 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
• 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
• 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
• 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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