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×

n

)p1(p

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”