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 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 = % 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 = 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”