t-Statistics and Correlation

sample mean should approximate population mean

Estimated standard error=square root of sample variance/ sample size

sm=square root of sample variance/sample

t-statistic is used when the population mean and variance are unknown

t-statistics are bell-shaped and symmetrical ttest-dist

null hypothesis states treatment has no effect

Hypothesis testing (4 parts)

  1. State hypothesis and select an alpha level
  1. Locate the critical region
  1. Calculate the test statistic
  1. Make a decision regarding hypothesis (H0)

Two assumptions for t-Statistic

  1. population sampled must be normal
  1. Values in the sample must have independent observations

Positive and/or negative signs depict the positive or negative direction of the relationship.

Perfect correlation: correlation of 1.0

intermediate values between 0 and 1 indicate the degree of tendency

Pearson correlation for a sample= degree to which X and Y vary together/ degree to which X and Y vary seperately

Correlation measures the degree of relationship between two variables on a scale from 0-1.0

Sum of products: measure the amount of covariability between two variables correlation-and-regression-10-638

A correlation does NOT necessarily imply a cause-and-effect outcome between two variables.

correlation-and-regression-33-638 Partial correlation measure relationship between two variables while observing/controlling the influence of a third variable by holding it constant