Stat 100 Work Chapter 20, Try Problems 1-9 Chapter 19, Try Problems 1-7 Read Chapter 4
Confidence Interval An interval of values that is likely to contain the population value The purpose is to use a sample to estimate a population characteristic. Interval is calculated as sample value ± margin of error
Prob. 12 of CH. 19. Part (a) Time Magazine survey: 59% of n=507 American Catholics favor allowing women to be priests Reported margin of error = 4.4% Find a confidence interval for the response to the question and write a sentence interpreting the interval.
Answer Sample value margin of error 59% 4.4%, which is 54.6% to 63.4% Interpretation: We can be 95% confident that between 54.6% and 63.4% of all American Catholics favoring allowing women priests.
Elements of problem Population = all American Catholics Sample = 507 Catholics in survey Value of interest = percent favoring women priests Sample value = 59% Estimate for population is 54.6% to 63.4%
Prob. 12, CH. 19, part (b) Calculate the confidence interval using the formula given in the book rather than the reported margin of error
More Exact Margin of Error for a proportion 95% m.e. =2×
For women priests question p=0.59, n=507 2 Sqrt [0.59 (1-.59)/507]=.044, or 4.4% Value is same as reported Interval is 59% ± 4.4%
Example pertaining to Ch. 20 For n=36 college women, mean pulse = 75.3 and SD=8. Based on this, determine a confidence interval for the population mean
Margin of error for mean Margin of error =2×SEM = 2 [SD/sqrt(n)] SEM=8/sqrt(36)=8/6=1.33 Margin of error = 2×1.33=2.7
Confidence Interval for Mean Pulse sample mean ±margin of error 75.3 +/-2.7 ; 72.6 to 78.0 95% certain that mean pulse for all women is between 72.6 and 78.
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?
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”