Quiz 6: STA 3032 - Midterm 2 Coverage and Hypothesis Testing - Prof. Chulmin Kim, Quizzes of Statistics

Download Quiz 6: STA 3032 - Midterm 2 Coverage and Hypothesis Testing - Prof. Chulmin Kim and more Quizzes Statistics in PDF only on Docsity! Quiz 6: STA 3032: Friday, Apr. l3 : Coverage-Midterm #2:Dr. Chulmin Kim * Normal and t-tables are on the back of this auiz. Last Name Only : Gl Score: 1^ 7 / l0 pts.-5T- I . Researchers are stuilying yield of a crop in three locations. The researchers are going to compute independent 80% cbnfidence intervals for the mean yield at each location. What is the probability that at Ieast orie of the intervals will cover the true mean yields at their location? [2 pts.l l,- .In 1 ' o x-L Use the following to ahswer questions 2-3: Do students tend to improve their SAT Mathematics (SAT-M) score the second time they take the test? A random sample of four students who took the test twice received the following scores. 4 : t--ra 500 q Student First score Second score I 350 440 1d 23 520 720 600 720 630 t: (a't\(6c) 0 74 Assume that the change in SAT-M score (second score - first score) for the population of all students taking the test twice is normally distributed. 2. a) Whatprocedure dowe use forthe data?llpt.l's!r","n' { :#;,? -'i" y -,.i b) What is a9}%oconfidence inter,"'al for p, themean change in SAT-M scole? [2pts.l bo: >ttt<W) bo: st-7+ X -l3. Suppose we do not believe that students tend to improve their SAT-M score the secofid time they take the test. Based on the confidence interval previously calculated,Ve wish to test flo: lFO versus H": trt*0 at t\e 5%o significance level. Determine which of the following statements is true: [pt.l a52W" cannot make a decision since the confidence level we used to calculate the confidence interval is 90Yo, and we would need a 95olo confidence interval. B) We reject Ho, since the value 0 falls in the 9A% confidence interval' C) We cannot make a decision since the confidence interval is so wide. r -r' Oj' We do not reject Flo, since the value 0 falls in the 9006 confidence inie{val and would therefore alsor--/ fall in the 957o confidence interval. { Use the following to answer questions,4-5: A sociologist is studying the effect of having children within the first two years of marriage on the divorce rate. Using hospital birth records, she selects a simple random sample of 200 couples who had children within the first two years of marriage. Following up on these couples, she finds that 80 couples are divorced within five years. Let p = the population proportion of couples who had children within the first two years of marnage and are divorced within five years. t -- | 7 Lt , 4 4' S,rppor" the sociologist wishes to test l{,s: p=l/2 versus Hu: p*l/2. ' + ( t- 'l) a) What is the P-value? 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