stas exam with 100% correct solutions 2024

α correct answersThe symbol for level of significance. β correct answersThe probability of failing to reject (accepting) a false null hypothesis. Alternative hypothesis correct answersThe hypothesis that the researcher wants to prove or verify; a statement about the value of a parameter that is either "less than," "greater than," or "not equal to." Approximate two-sample t test correct answersA test for comparing the means of two independent samples or two treatments where the test statistic has an approximate t distribution. The formula for computing degrees of freedom is complicated. ANOVA (Analysis of Variance) correct answersa statistical procedure for testing the equality of means using variances. Central Limit Theorem correct answersThe name of the statement telling us that when sampling from a non-Normal population, the sampling distribution of x¯ is approximately Normal whenever the sample is large and random. Claimed parameter value correct answersThe value of the parameter given in the null hypothesis. E.g., μ0 is a claimed parameter value. Conditions correct answersThe basic premises for inferential procedures. If the conditions are not met, the results may not be valid. Conditions necessary for a one-sample t procedure (using t* for C.I. or getting P-value from t table) correct answersNormality of the original population & SRS. (Note a t-distribution is robust with respect to nonnormality provided no outliers and no strong skewness. So, we can use a t-distribution procedure when n 40 provided the data have no outliers. We must have an SRS however.) Check (1) data collection and (2) if n 40, check for outliers in data plot; if n ≥ 40, apply CLThm. Conditions necessary for a two-sample t procedure (using t* for C.I. or getting P-value from t table) correct answersNormality of both populations & either stratified sample (independent SRS's) or random allocation. Check (1) data collection and (2) if n1 + n2 40, check for outliers in both data plots; if n1 + n2 ≥ 40, apply CLThm. Conditions necessary for matched pairs t procedure (using t* for C.I. or getting P-value from t table) correct answersNormality of population of differences & either SRS or random allocation. Check (1) data collection and (2) if number of pairs 40, check for outliers in plot of differences; if number of pairs ≥ 40, apply CLThm.