Unit 6 Flashcards
What are sig test used for
When do we use sig tests
Test a claim about the value of a population parameter
Decide whether the evidence supporting a claim is likely or unlikely to happen by chance alone.
Conditions of a 1 sample Z interval
what is it used for
Population proportion
SRS
n <= 10% of N
n = sample size, N = population size
Normality: n*phat >= 10 and n * (1-phat) >= 10. ‘Conditions of normality have been met’
General formula for confidence interval
Confidence interval = Point Estimate +/- Margin of error
= point estimate +/- (critical val)(standard error of statistic)
What does the margin of error describe
How much a value of a sample statistic is likely to vary from the value of the corresponding population paramet.er
Factors that affect the margin of error
what is it
How much statistic typically varies from the parameter
Sample size - larger the sample size, smaller the margin of error
How confident we want to be in our estimate.
Lower confidence level = lower margin of error.
Formula of margin of error
Critical value * Standard error of statistic
What is the standard error
Estimate of the standard dev of a sampling dist of the stat
What is the critical value
The absolute value of the Z score.
How to interpret the confidence interval
We are C% confident that the interval from _ to _ captures the [population parameter]
How to justify a claim using a CI
If all values of CI are consistent with claim - sufficient evidence
If one or more values of CI are inconsistent with claim - insufficient evidence.
How to interpret the Confidence level (prop)
In repeated random sampling with the same sample size, approx C% of “C%” confidence intervals will capture the population proportion
What is the null hypothesis
A claim of no difference or no change.
H0
What is the alternate hypothesis
Claim we hope to support with evidence from collected data
When is a one sample z test used
Test the claim about the proportion of successes
Conditions for a one sample z test for a population proportion
SRS
10% condition
N*p0 and N * (1-p0) >= 10
p0 is the prop specified by H0
General formula for tests
(Statistic - parameter)/standard error of statistic
Formula for 1 sample Z test
phat - P0)/sqrt(p0 * (1-p0)/n)
What is the significance level
what is it rep by
Alpha
Predetermined boundary value that we use to determine if a p-value is small or not small
What do p-values indicate
What do they do
Observed value of test statistic would be unusual if the null hypothesis was true
Provide statistical evidence for the alternate hypothesis.
Smaller the p value - more convincing statistical evidence for the alternate hypothesis
What happens if p-value is < alpha
What happens if p-value is > alpha
Reject H0. Sufficient evidence that Ha
Fail to rej H0. Insufficient evidence that Ha
What is a type I error
what is a type II error
generally what is more consequential
Null hypothesis is true and is rej (false positive)
Null hypothesis is false and is not rej
Generally type II error is more consequential
Probability of Type I error
Probability of Type II error
what is power
Prob of TI error = alpha
Prob of TII error = 1-power
power = probability that the test will correctly reject a false null hypothesis.
4 factos that affect power
Increasing sample size
Increasing alpha
Standard of error decreases
True parameter value is further from the null
Conditions for a 2 sample Z interval
Both samples are SRS Both samples <= 10% of respective populations Normality: n1*phat1 >= 10 n1* (1-phat1 >= 10 n2*phat2 >= 10 n2*(1-phat2 >= 10
Conditions for a 2 sample Z test
Both samples are SRS Both samples <= 10% of respective populations Normality: n1*pc>= 10 n1* (1-pc>= 10 n2*pc>= 10 n2*(1-pc>= 10
Conditions for all experiments
SRS
NORMALITY
NO INDEPENDENCE
Formula for 2-sample-Z-test
(phat1-phat2)-0 / sqrt(pc(1-pc)(1/n1 + 1/n2)
How to interpret the P value
Assuming Ho is true, there is a probability of getting a difference in proportions of or , by chance alone in the random assignment (random samples).
