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stat252 wint05 exam1

# stat252 wint05 exam1 - r-‘v “Ev-RTFAT 25202 Table No...

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Unformatted text preview: r-‘v “Ev-RTFAT 25202 Table No. _\ Exam 1--Blue '* __ I . _ _ 'w _ ' I; Winter, 2005 Name“ .V I, wk 00 ALL WORK AND SHOW ALL ANSWERS IN EXAM BOOK. START EACH PROBLEM ON A NEWPAGE IN BOOKLET. TURN IN THIS EXAM AND FORMULA SHEET WITH TEST. 1. A direct—mail company assembles and store paper products (envelopes, letters, etc.) for its customers. The company estimates the total number of pieces received in a shipment by estimating the weight per piece and then weighing the entire shipment. The company is unsure whether the sample of pieces used to estimate the mean weight per piece should be drawn from a single carton, or whether they should sample from a number of cartons. To make the decision, they took ﬁve random samples from each of six cartons. a) In your exam booklet put a completed AN OVA table, ﬁlling in all places where there is a (~) in the table shown below (c). (8 pts) b) Do steps 1-3, and 5 of a hypothesis test to determine if there are any signiﬁcant differences in the mean weights of pieces ﬁ'omthe six cartons. (7) pts) l c) Find the approximate P—value for the test statistic you found in part (b), and give your 1 practical conclusion using a = .05 (4 pts) One-way ANOVA: weight versus carton Source DF SS MS. F carton - 0.007782 -- -- Error - 0.008920 —~ Total - 0.016703 d) The analyst lost some of the output. However, he still has the values of the sample means, has the means arranged in order, and has some information ﬁom Tukey’s multiple comparisons. Using this information determine whichpnpulation means are signiﬁcantly diﬂ‘erent, andin which direction. (6 pts) Tukey 95% Simultaneous Confidence Intervals All Fairwise Comparisons among Levels of carton i Individual confidence level = 99.50% ’ Order of means: 1 6 3 5 ' 2 4 Value of means: 1.8474 1.8594 1.8716 1.877 1.8782 1.899 ﬂ__________________ﬂ_______*“__~___ﬂ_____._ carton = Carton}. subtracted from: carton Lower Center Upper CartonZ —0.00688 0.03030 0.06848 Carton3 -0.01348 0.02420 0.06188 e) How many paired comparisons- were possible and-whatwas the family errorrate for all your comparisons? (6 pts) Page 1 of’3 A local Irealtor wishes to estimate the mean sales price of all homes sold in the outlying areas of the city of San Luis Obispo in the last three months. She collected data on the sales price of sixteen different residential properties. Some of the results (as summarized in Minitab) are shown below. The values are in thousands of dollars. a. What is the point estimate of the means sales price of homes in the outlying areas of San Luis Obispo? (2 pts) b. She wishes her sample results to reﬂect sales of the last three months. How should she have chosen her sample? Hint: Do not merely say randomn—be speciﬁc with respect to the group she starts with, and how she chooses the homes in her sample. (5 pts) 0. She wishes to know the minimum value of the mean sales price, so you suggest ﬁnding a lower conﬁdence bound. Find a 90 % lower conﬁdence bound for the mean sales price. (8 pts) (1. Suppose the mean value for the previous three-month period was \$405,000. Using this value as the claimed value, write out the null and alternative hypothesis that you could test using the conﬁdence bound you found in part c. What would be the probability of a type I error associated with your test? (5 pts) One-Sample, T: SaIePrlce Variable N Mean StDev SalePrice r 16 449.788 322.506 There are seven sections of STAT 252 taught this quarter, two are in this studio-classroom, and ﬁve aren’t. I teach the two sections in the studio. One instructor teaches three sections (all not in the studio), while athird instructor teaches two sections, both not in the studio. Suppose my . department chair wants to test to determine if students taught in a studio environment score better, Hon average, than students not taught in a studio environment. He decides to randomly choose 15 students from the two studio sections at the end of the quarter and given them his test, and also choose 15 students ﬁ'orn the other ﬁve sections and give them his test, recording the scores on each individual in the two groups. a) What is the response variable in this study? (3 pts) b) What is the factor involved, and what are the factor levels? (5 pts) 0) What are the experimental units in this problem? Explain. (4 pts) d) Is this study a designed experiment? Why or why not? (5‘ pts) e) Would our samples be independent or paired? Explain (5 pts) (Go-to next page) Page 2 of 3 In California there is no law to demand that a cable-TV company face competition. A committee of the California Assembly wishes to study if companies with no competition charge, on average, more than \$4.00 more than companies with competition. To do the study they randomly chose eight areas where there was no competition and determined the rate in each of those eight areas. Then they chose eight areas where there was competition and determined the basic rate in those areas. The no-competition sample had a mean of \$28.65 and a standard deviation of \$2.50. The competition sample had a mean of \$21.46 and a standard deviation of \$3.30. a) Deﬁne the appropriate parameters and give the null and alternative hypotheses. (6 pts) b) What assumptions are necessary to do the above test? (4 pts) 0) Where possible, check the assumptions listed in (b). Be sure to give your conclusion. (4 pts) (1) Set up the test statistic to do the test for part (a). That is, put all the appropriate numbers in the test statistic formula, but don’t calculate a t—value. (8 pts) e) Suppose the calculated value of the test statistic is 2.18. ' Find the P—value and give the practical conclusion. (5 pts) Page 3 of 3 ...
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stat252 wint05 exam1 - r-‘v “Ev-RTFAT 25202 Table No...

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