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Stat 200 Week 6 Homework Solution Correct Answers

Week 6 homework answers for a statistics course.

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    Stat 200 Week 6 Homework Solution Correct Answers 2 . List 3 measures one can take to increase the power of an experiment. Explain why your measures result in greater power. 65. Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test. The null and alternative hypotheses are: a. Ho : =4.5, Ha : >4.5 b. Ho : μ ≥ 4.5, Ha : μ <4.5 c. Ho : μ =4.75, Ha : μ >4.75 d. Ho : μ =4.5, Ha : μ >4.5 77. An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees. Suppose you believe that the mean time is longer. You conduct a survey of 49 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2. Do the data support your claim at the 1% level? 83. According to an article in Newsweek , the natural ratio of girls to boys is 100:105. In China, the birth ratio is 100: 114 (46.7% girls). Suppose you don’t believe the reported figures of the percent of girls born in China. You conduct a study. In this study, you count the number of girls and boys born in 150 randomly chosen recent births. There are 60 girls and 90 boys born of the 150. Based on your study, do you believe that the percent of girls born in China is 46.7?

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    2. A company produces two products that are processed on two assembly lines. Assembly line 1 has 100 available hours, and assembly line 2 has 42 available hours. Each product requires 10 hours of processing time on line 1, while on line 2 products 1 requires 7 hours and product 2 requires 3 hours. The profit for product 1 is $6 per unit, and the profit for product 2 is $4 per unit. a. Formulate a linear programming model for this problem. b. Solve the model by using graphical analysis. Answer: a) formulation: X1 = amount of product 1 X2 = amount of product 2 Maximize 6X1 + 4X2 subject to: 10X1 + 4X2 <=100 7X1 + 3X2 <= 42 X1, X2 >=0 b)

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    I draw the feasible set which has 3 corners D(0,0), B(0,14), A(6,0) One of them is the optimal solution. Now if we check for which value 6X1 + 4X2 is maximum, if we check then we get (0,14) (i.e. X1 = 0, X2 = 14) for which 6X1 + 4X2 is maximum and the maximum value is 56. 6. The Pinewood Furniture Company produces chairs and tables from two resources – labor and wood. The company has 80 hours of labor and 36 board - ft. of wood available each day. Demand for chairs is limited to 6 per day. Each chair requires 8 hours of labor and 2 board - ft. of wood, whereas a table requires 10 hours of labor and 6 board - ft. of wood. The profit derived from each chair is $400 and from each table, $100. The company wants to determine the number of chairs and tables to produce each day in order to maximize profit. Formulate a linear programming model for this problem.

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