MAT 221 SS2 2020 Exam 2 Final Ver..pdf - MAT 221-M002 Exam...

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MAT 221-M002 Name: Exam II; Duration: 1 Hour Summer Session II 2020 ONLINE Instructor: Nicholas Ng Calculators may be used for arithmetic only. Do not use statistical functions in scientific calculators. Show as much work as possible for full credit. NO WORK = 0 POINTS! (Please Print/Work/Scan/Upload as a PDF file onto BB.) Important Formulae: r 1 n ´ 1 „ˆ x 1 ´ ¯ x s x ˙ ˆ y 1 ´ ¯ y s y ˙ ` ¨ ¨ ¨ ` ˆ x n ´ ¯ x s x ˙ ˆ y n ´ ¯ y s y ˙ Least Squares Regression Line: ˆ y b 1 x ` b 0 where b 1 r s y s x and b 0 ¯ y ´ b 1 ¯ x . Residual at a data point p x, y q is y ´ ˆ y Observed y value at x ´ Predicted y value at x . Sampling distribution of sample means X from SRS’s of large enough sample size n , we get X N ˆ μ, σ ? n ˙ . Sample count and sample proportion are denoted by X and ˆ p X n , respectively. If X has a binomial distribution, it is denoted X B p n, p q . Given X B p n, p q , if np ě 10 and n p 1 ´ p q ě 10, we get sampling distribution of sample counts X N p np, a np p 1 ´ p qq and sampling distribution of sample proportions ˆ p N ˜ p, c p p 1 ´ p q n ¸ for sample proportions. Problem Points Score 1 28 2 10 3 12 4 16 5 12 6 10 7 12 Total 100 1
1. (28 points) (a) (2 points) Suppose we are given a least squares regression line ˆ y “ ´ 43 x ` 10 obtained from data where the range of data for the explanatory variable ranges from a minimum value of 3 to maximum value of 40. If we were to find the predicted value at x 56, we would be from the data.
(b) (2 points) Suppose we wanted to know the average salary of SU professors. We first separate all professors at SU into their respective departments and then perform a SRS of size 10 from each department and take the average of the salaries from each sample. This sampling method is an example of .
(c) (2 points) Suppose you have have quiz you did not study for that consists of 10 true or false questions. If you need at least a 70% to pass, what is the probability that you will pass if you randomly guess on each true or false question? (Hint: What is the probability of success; what is the probability that you’ll randomly guess a true or false question correctly? How many problems out of 10 constitutes a pass?)

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