Proportions

Confidence Intervals

100

Conditions for creating a confidence interval

Random, Independent, and Normal

200

The critical value for a 90% Confidence level

z*=1.645

300

Formula for the confidence interval 

point estimate +/- (critical value)*(standard error)

400

The phrasing of the confidence interval conclusion

We are C% confident that the true proportion of the population parameter is between...

500

x=15, n=45, C%=.92

Assume all conditions are met. Construct a 92% confidence interval. 

(0.2103, 0.4564)

Margin of Error

100

As this gets larger, the Margin of Error gets smaller

Sample size

200

As this decreases, the margin of error decreases and our interval gets narrower

Confidence level

300

Formula for margin of error

(critical value)*(standard error)

400

Interpreting C% and factors affecting Margin of Error

In repeated sampling with the same size, approximately C% of "C%" confidence intervals will capture the population proportion

500

x=180, n=400

If you want to create a confidence interval of 0.45 ± 0.04, what degree of confidence should you use?

normalcdf(−1.608, 1.608, 0, 1) = 89.2%

Significance Test

100

Significance level when C%=0.95

5%

200

The hypothesis when p is above or below the assumed population proportion

Alternative Hypothesis

300

The amount of standard deviations the sample proportion is from the null value

test statistic

400

In a significance test of H0:p = 0.75 vs H0:p=/=0.75, a random sample of 90 obtained p̂= 0.82. What is the p-value in a one sample z test for proportions?

p-value = 0.1260

500

H₀: p = .8       x: 41

H_a: p < .8       n: 60

Assume all conditions are met. Construct a test at a 5% significance level. Find test statistic and p-value.

z = -2.26

p = 0.012

Errors and Powers

100

We fail to reject the null when we were supposed to reject it.

Type II Error

200

The probability of rejecting a false null hypothesis

Power

300

The higher the power, the ____ Type II error is

lower

400

Two things that increase the power of a significance test

Sample size and significance level

500

If a hypothesis test is found to have power = 0.70, then what is the probability that the test will result in a Type II error?

0.30

Difference in Proportion

100

Combining variables from a normal distribution results in a ____.

Normal Distribution

200

Appropriate confidence interval for a difference between two proportions

two-sample z interval for a population proportion

300

The mean of the sampling distribution for a difference in proportions can be found through this formula

p₁-p₂

400

Interpret the confidence interval for a difference in proportions

We are C% confident that the true difference between the proportion...

500

x₁=460, n₁=800

x₂=520, n₂=1000

Assume all conditions are met. Give a 99% confidence interval for the difference between the two proportions.

p-value = 0.00995

CI = (-0.0057, .11569)