STA 207 Final, Spring 2010

Sta207 Final exam Question 1 [21 points] The scholastic aptitude test (SAT) is an exam designed to help assess the aptitude of a candidate to pursue higher education. The international percentages of scores as posted by the higher education journal for year 2000 came as follows: SAT Scores International % 0 -< 350 11% 351- 450 35% 451-550 30% 551-650 19% >650 5% In an attempt to compare the SAT percentage distribution in Lebanon with the international distribution, the SAT scores of 200 candidates were recorded then arranged in the following frequency table: SAT Scores for Lebanese Candidates Number of students 0 -< 350 23 351- 450 65 451 —550 58 551-650 38 >650 16 a) Test whether the distribution of SAT scores for the Lebanese candidates corresponds to the SAT scores of International students. Use a= 0.05. [9] b) LUB is a selective university located in Lebanon that requires an SAT score of higher than 550 to accept a student in its business school. Suppose the above 200 students applied to enter the business school of the above university, test whether less than 30% of the above students would be admitted. Use a= 0.01. [9] c) Calculate the p-value of the above test. [3] Question 2 [35 points] In an attempt to understand whether the years on the job affects the efficiency of workers measured by the weekly production (in hundreds of items), a random sample of 5 workers were selected and their years on the job as well as their weekly production were recorded as follows: Years on Job Weekly Production (100 items) 14 6 7 5 3 3 15 9 11 7 Let the years on the job be the independent variable X and Weekly Production the dependent variable Y a) Find the Least Square Regression Line [7] b) Interpret in the context of the problem the regression slope and intercept. [3] c) Fora person who has been on the job for 7 years, what would be his expected weekly production. Does the regression line overestimate or underestimate reality at this point? Why [3] d) Determine the coefficient of determination and interpret its meaning. [4] e) Construct a 90% Confidence Interval for the population regression slope. [8] f) Interpret the above interval in the context of the problem. [2] g) If you are to test whether there is a positive relationship between the years on the job and the productivity without limiting yourself to a specific a. Conduct the above test using the p-value approach. [4] h) Using your p-value, what would your conclusion be if @ =0.005? What if a =0.1? Justify [4] Question 3 [44 points] Is there a difference in the percentage of college men versus college women who smoke more than one pack per day? A random sample of 400 women revealed 72 of them who smoked more than 1 pack per day. A sample of 500 men revealed that 70 smoked more than a pack per day a) Construct a 95% Confidence Interval for the difference between the proportion of men and the proportion of women who smoke at least a pack of cigarettes a day. [9] b) Using the above interval, can you make an inference on whether there is significant difference between the proportion of College Men and College Women who smoke more than 1 pack of cigarettes a day? Justify. [3] c) The study resumed by asking the 72 women smokers and the 70 men smokers sampled above about the number of cigarettes smoked per day. The results came as follows: Women Smokers Men Smokers Mean Number of 30 38 Cigarettes per day (x) Standard deviation (s,) 3 a Test whether the college Men smoke more than college Women by more than 6 cigarettes a day (i.e. one third of a pack) Use a= 0.025. [9] d) Test at a= 0.025 whether College heavy smokers (those who smoke more than one pack, men and women combined), smoke more than 33 cigarettes per day knowing that the average number of cigarettes for the 142 students sampled above is 34 cigarettes and the standard deviation is 2.7 cigarettes. [8] e) Calculate the B error of the above test if the true average number of cigarettes for college student is 34. [7]