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

n

pp )1(2

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 = n

pp )1(3

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”