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Unformatted text preview: STAT 252-02 Table No.
Exam 1--Yellow . . _' ~ g . - I Winter, 2005 Name 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 seven random samples from each of ﬁve 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 from the Sigcai'tons. (7) pts) @7 Find the approximate P-value for the test statistic you found in part (b), and give your
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 from Tukey’s
multiple comparisons. Using this information determine which population means are
signiﬁcantly different, and in which direction. (6 pts) Tukey 95% Simultaneous Confidence Intervals
All Pairwise Comparisons among Levels of carton Individual confidence level = 99.50% Order of means: 1 3 5 2 4
Value of means: 1.8474 1.8716 1.877 1.8782 1.899
carton = Cartonl subtracted from: carton Lower Center Upper M SD: U‘ppﬂr/(jjﬁlﬁr : sowg Carton2 —0.00688 0.03080 0.06848
Carton3 —0.0l348 0.02420 0.06188 6) lilow many paired comparisonsvwere‘possible and what was the family error rate for all
your comparisons? (6 pts) Pagel of3 A local realtor wishes to estimate the mean sales price of all homes sold in the outlying areas
of the crty of San Luls Oblspo 1n the last threemonths. She collected data on the sales price of ~ twenty 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) ’ 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 random——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 minimumvalue of the meanmsales price, so you suggest ﬁnding
a lower conﬁdence bounErFind a 95 % loWer conﬁdence bound for the mean sales
price. (8 pts) ‘ . Dona . _
@ Suppose the mean value for the prevrous three—month period was E 425,000) Usrng th1s
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: SalePrice Variable N Mean StDeV
SalePrice 20 449.788 322.506 There metﬁgnkectiom of STAT 252 taught this quarter, Mare—inthis studio classroom, and
Mt. I teach the Monsectigns in the studio. One instructor teaches “ﬂung sections (all not in the/studio), while a thirdv'instructor teaches two sections, both not “iﬂnwt—he studio. Suppose my department chair wants to test to determine if sngntstgught in a studio environment score better, ‘on ave e s A not tau t ' 'o e ' ent. 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 “F \ S
choose 15 students ﬁom the other ﬁve sections and give them his test, recording the scores on each individual in ,the two groups. N7}! 9 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 kﬂx l >114}! 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 116366” "’eti'tion’Char‘ on average, W
more than $5.00 more th com ames w1th com et1 1on. o o the study they randomly chos. .
areas where there was no competition and determined the rate in each‘of those areas. Then
they choseéeinareas where there wasicompetitiiiﬁt and determined the basic rate in those areas.
The no-competition sample had a mean of $28.65 and a standard deviation of $3.50. The
competition sample hadaurneanof $21.46 and a standard deviation of $3.90. 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) d) 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 1.32. Find the P-value and give the
practical conclusion. (5 pts) Page 3 of 3 ...
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- Winter '05