Chapter 8: Estimating Proportions With Confidence

Question 1

Define Point Estimator

Answer 1

a statistic that provides an estimate of a population parameter

Question 2

Define Point Estimate

Answer 2

the value of a point estimator from a sample. Ideally, a point estimate is out “best guess” at the value of an unknown parameter

Question 3

Define Confidence Interval

Answer 3

for a parameter has two parts:
point estimate ± margin of error

Question 4

Define Margin of Error

Answer 4

tells how close the estimate tends to be to the unknown parameter is repeated random sampling

Question 5

Define Confidence Level

Answer 5

C, which gives the overall success rate of the method for calculating the confidence interval

The interval computed from sample data will capture the parameter C% of all samples

Question 6

Interpretation of Confidence Level

Answer 6

If we select many random samples of size __n__ from the population, __C__% of the confidence intervals created will capture __the parameter context__.

Question 7

Interpretation of Confidence Interval

Answer 7

We are __C__% confident that the interval from _______ to ______ captures the (parameter).

Question 8

How to decrease Margin of Error

Answer 8

1. decrease confidence level
   and/or
2. increase sample size

Question 9

Formula for Calculating a Confidence Interval

Answer 9

statistic ± critical value * standard deviation of statistic

critical value: makes interval wide enough to have the stated capture rate

Question 10

What would happen to the length of the interval if the confidence level were increased to 99% from 90%?

Answer 10

longer because critical value increases

Question 11

What would happen to the length of a 90% confidence interval if the sample size was increased to 100 from 40?

Answer 11

shorter because standard error decreases

Question 12

One-Sample z Interval for a Population Proportion

Answer 12

p hat ± Z* x sqrt ( (p hat (1-p hat))/n )

Z* is always positive [ invNorm]

Question 13

Standard Error

Answer 13

sqrt ( (p hat (1-p hat))/n )

(margin of error) / (Z* * sqrt ( (p hat (1-p hat))/n ) )

Question 14

Conditions for Constructing Confidence Interval for a Population Proportion

Answer 14

Random: a random sample was taken
10 % - n < 1/10 N when sampling without replacement
Large count - n*phat ≥ 10 and n(1-phat) ≥ 10

Question 15

Interpretation of Standard Error of p hat

Answer 15

In repeated SRSs of size ______, the sample proportion of __context__ typically varies from the population proportion by about __standard error__.

Question 16

Sample Size for Desired Margin of Error

Answer 16

(Z* * sqrt ( (p hat (1-p hat))/n ) ) ≤ margin of error –> solve for n.

If p hat is not given, use 0.5 as p hat. because it is the largest value of p hat (1-p hat). therefore gives you the largest sample size you need.

Question 17

Estimating the True Proportion (p)

Answer 17

State
Plan
Do
Conclude

Question 18

Two-Sample Z Interval for the Difference Between Two Proportions

Answer 18

(p hat 1 - p hat 2) ± Z* x sqrt ( (p hat 1 (1-p hat 1))/n 1 + (p hat 2 (1-p hat 2))/n 2 ) )

• standard error = sqrt ( (p hat 1 (1-p hat 1))/n 1 + (p hat 2 (1-p hat 2))/n 2 ) )
• margin of error = (p hat 1 (1-p hat 1))/n 1 + (p hat 2 (1-p hat 2))/n 2 )

Question 19

Conditions for Constructing Confidence Interval for Difference in Proportions

Answer 19

Random: independent random samples or two groups randomly assigned to treatments
10 % - If sampling without replacement => n1 < 1/10 N1 and n2 < 1/10 N2
If it is an experiment = doesn’t have to check 10 %
Large count - n1phat1 ≥ 10 and n1(1-phat1) ≥ 10 and n2phat2 ≥ 10 and n2(1-phat2) ≥ 10