MAT222-2007Spring

# MAT222-2007Spring - M AT 2 22 F inal A May 7,2007 N ame I...

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/ MAT 222 Final A (May 7,2007) Name: _ Instructor: _ *************** 1. There are 7 problems and a total of 9 pages in this booklet. 2. Show all of your work and label your answers clearly. 3. If you use a table, state the table used: for example 1.887 (from Table A). 4. you use a function on the TI 83 (or TI 89), write out the command you entered as well as the result: for example, 0.0668 (normalcdf (-10, -1.5, 0.1)). E 1 16 2 14 3 15 4 25 5 12 6 10 7 8 I Total ~,----- 1

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1. (16 pts) Based on a survey to compare females and males on the number of hours a day that they watched TV, the following summary statistics are obtained: (a) Is there a significant evidence that females spend more time on watching TV? Carry out a significance test at the 5% level of significance. (b) Give a 95% confidence interval for the difference between the mean TV watching time for females and the mean time for males. 2
2. (14 pts) A blind experiment was conducted for 49 college students for their preference between Coke and Pepsi. Twenty nine students preferred Coke, while the rest chose Pepsi. (a) Find a 95% confidence interval for the proportion of college students who prefer Coke to Pepsi. (b) Do the results provide good evidence that a majority prefers one of the drinks? Explain why or why not. (c) How large a sample would be required to obtain a margin of error of ±O.lO in a 95% confidence interval for the proportion of those who prefers Coke? 3

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3. (15 pts) Schering Corporation reported in their 1990 advertisement for Claritin, the allergy drug, that in a pediatric randomized clinical trial, 4 of 188 patients on Claritin showed symptoms of nervousness, while 2 of 262 patients taking placebo expressed nervousness. (a) Summarize the data in the following 2 x 2 table. Treat met Nervousness Yes No Claritin Placebo (b) Analyze the two-way table. State the hypotheses, calculate the X 2 statistic, degrees of freedom, P-value and your conclusion. 4
4. (25 pts) A study was conducted on the relationship between sales revenue y (in thousands of dollars) and advertising expenditure x (in thousands of dollars) for fast-food chain restaurants during a 3-month period. A sample of 15 locations yielded the following summary statistics: x = 14.10, Sx = 0.218, L(Xi - x)2 = 0.667; f) = 1420.50, Sy = 13.10; r = 0.875; S = 6.572 (a) Using the given summary statistics, find the least squares regression line. (b) Suppose that p is the population correlation between x and y. Carry out the test for Ha : p = 0 versus H a : p > 0, and draw your conclusion at the 5% level of significance. 5

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(c) State the null and alternative hypotheses in (b) in terms of the regression slope, (31, and conduct a significance test at 0: = 0.05. (d) Find a 95% confidence interval for the mean sales revenue when x* = 18.0. 6
5. (12 pts) According to an alumni survey, the starting salaries (in thousands of dollars) and the five majors (computer science, nursing, business, liberal arts, early childhood education) of recent graduates of a local State University are summarized as follows: Computer Science Nursing Business Liberal Arts Early Childhood Education ti 6 5 7 3 4 .'£ 34.63 30.14 35.59 24.57 24.63 s 3.58 1.51 2.83 3.55 2.51 (a) Complete the ANOVA table. Source DF SS MS F College Groups Error 515.91 * * * Total 681.32 * * * * * * (b) State the null and alternative hypotheses for the ANOVA F-test. (c) Draw your conclusion at a = 0.05.

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MAT222-2007Spring - M AT 2 22 F inal A May 7,2007 N ame I...

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