Conditions for performing a significance test about a mean
- Random: the data comes from a well-designed random sample or randomized experiment
- 10%: when sampling without replacement, check that n≤1/10N
- Normal/Large Sample: The population has a Normal distribution or the sample size is large (n ≥ 30). If the population distribution has an unknown shape and n<30, use a graph of the sample data to assess the Normality of the population. Do not use t procedures if the graph shows strong skewness or outliers.
Critical value t formula: T = (x̄-µ0)/(Sx/√(n))
When the population is normal, the distribution of the t statistic is exactly a t distribution with n-1 degrees of freedom.
To calculate areas under a t distribution curve using your calculator: 2nd -> VARS -> TCDF
When conditions are met, we can test a claim about the population mean μ using a one-sample t test for mean.
Suppose the conditions are met. To test the hypothesis H0 = μ = u0, compute the one-sample t statistic.
T = (x̄-µ0)/(Sx/√(n))
Find the p-value by calculating the probability of getting a t statistic this large or larger in the direction specified by the alternative hypothesis Ha in a t distribution with df = n - 1.
To perform a one-sample t test using your calculator: STAT -> TESTS -> T-Test
Interpreting confidence level:
If we were to make many random samples of [variable], about C% of the resulting intervals would capture the true [variable] of the population.
Test statistic t: t= (x̄-u0/(Sx/√(n))) Confidence Interval: x̄±t(Sx/√(n)))*