Stat 100, This week

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# Stat 100, This week - PowerPoint PPT Presentation

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
• 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
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
• Margin of error =
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%.
• 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?