The Basics
What is a null hypothesis?
A null hypothesis (H0) is a hypothesis, which in a significance test we try to reject. We assume this hypothesis is true during our test.
What is an SRS?
Simple Random Sample. A random sample where every possible sample of n objects is equally likely to occur.
What are the steps for conducting a confidence interval?
Population Parameter
Conditions
Test Statistic
Calculations
Conclusion
What is the expected value formula for Chi-Squared GOF Test, and the expected value formula for Tests of Homogeneity and Independence?
GOF Test: E=np Tests for Independence/Homogeneity: E= (row total)(column total)/table total
What parameter is the statistic, y-hat=a+bx, predicting?
y-hat=∝+βx
What is the general formula for confidence intervals?
CI=Statistic +/- Critical Value * SD(of statistic)
What are the conditions for one-sample z test for a proportion?
BONUS: How does this change for a mean?
Explain the difference between a paired t test for a mean difference and a two-sample t test for a difference in means. What are some tips for distinguishing between the two?
1) If data sets have unequal sample sizes, they cannot be paired.
2) If the data table has a third row or column with differences, they are likely paired.
3) Questions for paired data typically use "mean difference," while questions about two independent samples typically use "difference in means."
What is the expected score for male republicans?
Voting Preferences Male Female
Republican 200 150
Democrat 250 300
Independent 50 50
E=(500)(350)/1000=175
How is the population parameter defined in a t-test for slope?
ß = true slope of the population least-squares regression line predicting y=_____ from x=______
What is the central limit theorem?
The sampling distributions of the sample means will tend to follow a normal distribution if the sample size is large enough (n≥30).
What are the conditions for two-sample means tests?
BONUS: How does this change for an interval?
What are Type I and Type II errors?
Type I: When you reject the null when the null is true Type II: When you fail to reject the null when the alternative is true
What are the null and alternative hypotheses for a GOF Test?
H0: p1 = ____, p2 = ____, ... , pn = ____
Ha: At least one of the above population proportions is incorrect
What is the test statistic formula for a confidence interval for the slope of a population regression line?
t= b +/- t*(s/[sx√(n-1)])
What does df stand for, and when are they used?
Degrees of freedom are used in t-intervals and t-tests (and Chi-Squared tests).
What are the conditions for χ² Tests?
1) Simple Random Sample?
2) Is the 10% condition met?
3) Are all expected values are at least 5?
How do we find the minimum sample size to achieve a certain margin of error?
(critical z or t value)(standard error) ≤ ME
What are the null and alternative hypotheses for a Independence Test?
H0: There is no association between [the two variables].
Ha: There is an association between [the two variables].
Other possible answer (null: independent, alt: not independent)
What is the formula for degrees of freedom for Slope Intervals/Tests?
df=n-2
What is the difference between using z* and t*?
We use t* when estimating a parameter from sample data that does not include the population standard deviation.
What are the conditions for a linear regression test and confidence interval?
1) Simple Random Sample? (Stated)
2) Is sb = s/[sx√(n-1)]) (n < 10% of N)
3) Linear? (Scatter plot appears linear, resid plot shows no clear pattern)
4) Is samp dist of b approx norm? (Boxplot/histogram of residuals shows no strong skewness of outliers)
5) Equal SD? (resid plot shows no < or > pattern)
What is a combined p-hat? When is it used?
pc=(x1+x2)/(n1+n2)
Two sample z test for a proportion
What are the null and alternative hypotheses for a Chi-Squared test of Homogeneity?
H0: There is no difference in the population distributions of _______ for _______
H0: There is a difference in the population distributions of _______ for _______
What is the null hypothesis for a Linear Regression Significance Test?
H0: ß=0