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# PQ3 - STA 2023 Practice Questions Final Exam STATISTICAL...

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STA 2023 Practice Questions Final Exam STATISTICAL INFERENCE TABLE: (GIVEN on the test) Case parameter estimator standard error Sampling Distribution one mean x n s t (n-1) Mean of matched pairs difference d d x d s n t (n-1) difference of two independent means 2 1 2 1 x x 2 2 2 1 2 1 n s n s t with conservative df = smallest of (n 1 -1) and (n 2 -1) one proportion p p ˆ CI: ˆ ˆ (1 ) p p n ST: n p p ) 1 ( 0 0 z difference of two independent proportions 2 1 p p 2 1 ˆ ˆ p p CI: 1 1 2 2 1 2 ˆ ˆ ˆ ˆ (1 ) (1 ) p p p p n n ST: 2 1 1 1 ) ˆ 1 ( ˆ n n p p z McNemar YN NY TS YN NY OR NY YN TS YN NY NEED TO KNOW: Confidence Interval : estimator +/- (t or z) est. standard error Test Statistic: # ( ) o estimator from H t or z estimate of stderr

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Questions 1 – 4 An education researcher has developed a new technique to teach Spanish to high school students. To prove this new method is better, she will teach two groups of students for an entire semester, one with the new method and one with the standard method used today in high schools. She wishes to obtain 12 sets of identical twins, 24 people total, and split the twins up so that one of each twin is in Class 1, which will receive the new technique, and one is in Class 2, which will receive the old technique. At the end of the semester both classes will take a standardized exam and the results will be compared. 1. What method should be used to analyze this data? a) one mean b) two independent means c) matched pairs d) two independent proportions 2. What should our hypotheses be to test if your new method is better than the old method? a) H 0 :  2 = 0 vs. H A :  2 < 0 b) H 0 : D = 0 vs. H A : D < 0 c) H 0 :  2 = 0 vs. H A :  2 0 d) H 0 : D = 0 vs. H A : D 0 3. What distribution would you use to look up the p-value for this test of hypothesis? 4. Suppose we collect the data from this experiment and we find a p-value of 0.009. Which of the following is our conclusion at any reasonable alpha level?