One-sample t-test

Relationship between CI and Hypothesis Testing

If (1-alpha)%CI does NOT include μo from Ho then a test statistic(e.g., z-test) will be significant and vice versa.

df for one-sample t-test

df= N-1 - increase df, decrease difference between standard normal and t-distributions. -small df, large difference between t- and z-distribution curves.

One-sample t-test

used to compare a sample mean to a hypothesized value when the population variance of a variable is UNKNOWN.

t-critical

****since t-distribution has a heavier tail, the t-critical value is greater than z-critical value. -As decrease t-critical, increase df

effect size

-Cohen's d -amount of difference in standard deviation -the effect size from one-sample z-test can also be used in one-sample t-test with one modification (?)

t-distribution

-there isn't one t-distribution, but a family of t-distributions distinguished by df. -symmetrical distribution similar to the standard distribution but has a heavy tail(more likelihood of extreme scores)

Confidence Interval

-when an interval estimate is accompanied by a specific level of confidence (or probability) ***(1-alpha)% CI of a statistic is a confidence interval which (1-alpha)% of the statistic would fall if a study was repeated infinite times.

Width of CI

Width of CI is affected by confidence level and standard deviation: -As Confidence Level increases, width of CI increases -As StdDev increases, width of CI increases For a mean with a known StdDev, a StdDev is a standard error of the mean: -As N increases, Std error of mean decreases -As StdDev increases, Std error of the mean increases

One-sample z-test

used to compare a sample mean to a hypothesized value when the population variance of a variable is KNOWN.