STT 231 EXAM 3 STUDY GUIDE 2026/2027 ACCURATE QUESTIONS WITH CORRECT DETAILED SOLUTIONS || 100% GUARANTEED PASS NEWEST VERSION

STT 231 EXAM 3 STUDY GUIDE 2026/2027 ACCURATE QUESTIONS WITH CORRECT DETAILED SOLUTIONS || 100% GUARANTEED PASS NEWEST VERSION 1. Types of Confidence Intervals - ANSWER - one proportion - one mean - difference in proportions - difference in means 2. bigger confidence level - ANSWER wider 3. bigger sample size - ANSWER narrower 4. adding a constant - ANSWER same width 5. interpretation of confidence interval - ANSWER ONLY ONE CORRECT ANSWER "we are 95% confident the true parameter is between..." 6. Hypothesis Test for Difference in Proportions - ANSWER pi1 - pi2 7. conditions: - independent observations - 10 successes and 10 failures in BOTH groups 8. Hypothesis Test for Difference in Means - ANSWER mu1 - mu2 9. conditions: - independent observations - populations should be normally distributed or both sample populations should be greater than or equal to 25 10. Chi-Square is used when... - ANSWER there are two categorical variables Ho: variables are independent Ha: variables are related 11. Chi-Square Degrees of Freedom - ANSWER df = (rows - 1)(columns - 1) 12. Chi-Square Goodness of Fit - ANSWER used when comparing observed vs expected 13. Key Rules for Chi-Square - ANSWER - values are always positive - distribution is right-skewed - need expected count of greater than or equal to 5 14. effect size for proportions - ANSWER h - hat 15. effect size for means - ANSWER d - hat 16. Chi-Square Test of Independence - ANSWER - a statistical test in which both variables are categorical - tells us if the distribution of participants across categories is different from what would happen if there were no differences between the groups 17. How can we get one-mean confidence interval in R? - ANSWER 18. What is the relationship between confidence intervals and two-tailed hypothesis tests, and what are the key limitations of this correspondence? - ANSWER A confidence interval with level 1−α1−α corresponds to the set of parameter values that would not be rejected in a two-tailed hypothesis test at significance level α (i.e., would produce p-values ≥ α). However, this relationship is approximate and only applies to two-tailed (non-directional) hypothesis tests 19. What is the equation for margin of error? - ANSWER s/√n (s = sample sd, n = sample size) 20. What is single proportion - ANSWER π 21. what is single mean - ANSWER µ 22. What is the sampling distribution of a difference between sample proportions? - ANSWER π-hat1 - π-hat2 23. What 2 conditions must be met for sampling distribution (pi-hat1 - pi-hat2) to be modeled by normal distribution? - ANSWER Both samples (n1 and n2) must be large (success-failure assumption), and observations must be independent and identically distributed within and between samples 24. What is a two-proportion z-test - ANSWER Hypothesis test that compares the rate or proportion (P) across two independent groups 25. What is the test statistic of two-proportion z-test - ANSWER pi-hat of c = # of success / # of cases 26. What 2 conditions must be met for sampling distribution (x-bar1 - x-bar2) to be modeled nearly normal? - ANSWER Both samples (n1 and n2) must be large (success-failure assumption) OR both samples be ≥ 25, and observations must be independent and identically distributed within and between samples 27. first condition of hypothesis test - ANSWER 10 successes/failures 28. second condition of hypothesis test - ANSWER independence of data points 29. if value is contained in interval - ANSWER accept null, p-val greater than significance level 30. if value NOT contained in interval - ANSWER reject null, p-val smaller than significance level 31. chi sq goodness of fit - ANSWER 1 categorical variable follows proposed distribution 32. chi sq center - ANSWER df 33. df - ANSWER (rows-1)(columns-1) 34. chi sq intependence test - ANSWER 2 categorical variables 35. expected count - ANSWER row total x column total / table total 36. H0 of independence test - ANSWER variables are independent 37. HA of independence test - ANSWER variables are associated 38. chi sq test stat - ANSWER (obs - exp)2 / exp 39. interpretation of p-value with chi sq - ANSWER probability of witnessing test stat or higher under assumption H0 is true 40. increasing n - ANSWER df stays same 41. test statistic increases - ANSWER increasing n 42. ANOVA - ANSWER comparing the means of two or more groups 43. first condition of ANOVA - ANSWER observations are independent 44. second condition of ANOVA - ANSWER samples drawn from normally distributed population 45. third condition of ANOVA - ANSWER when evidence for HA, no comment on which groups are different 46. F statistic - ANSWER between group variability/within group variability 47. larger F stat - ANSWER more evidence against null