Inference Key Questions

What is the meaning of p-value? A p-value is the likelihood of your sample happening by chance alone if Ho were true. Higher p-value = more likely to occur by chance Ex. A p-value of .05 means that the event in question will occur 5% of the time, given Ho is true.

What is the meaning of a confidence interval in context? I am 95% confident that my interval captured the true (mean, proportion, difference of means, difference of proportions) because the process I used works 95% of the time.

Name the 7-10 major tests we run. 1 Sample T Test (also used for matched pairs) 1 Prop Z Test 2 Sample T Test 2 Prop Z Test Χ2 Test for Independence Χ2 Test for Homogeneity Least Squares Regression Chi-square GOF

Name the confidence intervals we run. T- interval 1 Prop Z-interval 2 Sample T-interval 2 Prop Z-interval

What is the difference between a ‘Z’ and a ‘T’? Use ‘Z’s when you know the standard deviation or when the sample size is extremely large (1000s). Use ‘T’s for everything else.

Name the symbols that we use in these tests for the null hypothesis and the alternative. Null Hypothesis: Ho Alternative Hypothesis: Ha

Name the test statistic variables Parameter Variables μ- population mean Π (P)- population proportion σ- population standard deviation Sample Variables X- sample mean P- sample proportion S- sample standard deviation

Name the conditions for all seven tests. Chi Square Least Squares Regression Proportion (T+Z) Mean (Z+T) E- 80% of expected cells are >5 I- Independent S- SRS A-and R- Residual plot is randomly scattered N- NP>10 N(1-P)>10 A- and N- Normal Distribution I- independent P- Less than 10% of the population sampled

Describe the central limit theorem. The central limit theorem states that large sample sizes will produce a normal curve for the sampling distribution of x-bar or p-hat.

Z*(s/√n)= margin of error Z*(√(p)(1-p)/n = margin of error How do you calculate the number of samples needed for a mean or proportion? Z*(s/√n)= margin of error Z*(√(p)(1-p)/n = margin of error

If you want to cut the margin of error in half, how many samples should you have? To cut margin of error in half, you need to quadruple the sample size.

What is a type I error, and what are the consequences? Essentially a ‘false positive’ Ho is true, but you found otherwise/

What is a type II error, and what are the consequences? Essentially a false ‘negative’ Ha is true, but you failed to detect that.

What is power? The probability that the test will reject the null hypothesis when the null hypothesis is false. The value of β

What is the relationship between alpha, beta, and N?

When do you pool? When the standard deviations are the same.

What are the reference numbers for all the different confidence intervals? 1 sample T test---given number is problem. Matched pairs T test—zero 2 sample t test---zero 1 proportion Z test---given proportion in problem. 2 proportion Z test--- zero

What do bias and variability mean? Bias is how far off your statistic is from the parameter. Variability refers to how "spread out" a group of scores is.

What is the parameter of interest? The statistical parameter is the context of the variable you are interpreting.

Name TWO ways to shrink the confidence interval Increase the sample size decrease Confidence level