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Final

MGMT 1050 - Final exam 06.doc

10 Pages
171 Views
Fall 2013

Department
Management
Course Code
MGMT 1050
Professor
William(bill) Woof
Study Guide
Final

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Part I - Problem Recognition (24 marks, 3 marks each) – 2 for hypotheses, 1 for test
ALEX
1.
A ski company in Whistler owns two ski shops, one near
Whistler and one near Blackcomb. The following data were
collected from both stores:
Whistler
shop
Blackcomb
shop
Mean sales $328 $435
Sample std. Dev. $104 $151
Sample size 35 days 30 days
The company would like to test for a difference in daily
average goggle sales between the two stores
H0: µw − µB = 0
HA: µw − µB ≠ 0
Test: t test
Not equal variance
2.
The state lottery office claims that the average household
income of those people playing the lottery is greater than
$37,000. They also know that the distribution of these
households’ income is normal with a standard deviation of
$5,756. To test their claim a sample of 25 households was
studied. It was found that the average income in the sample
was $36,243.
H0: µ < 37,000
HA: µ > 37,000
Test: Z test
3.
In random samples of 1000 people in the United States and
in France, 70% of the people in the Unites States and 75%
of the people in France indicated that they were positive
about the future economy. Does this provide strong
evidence that the people in France are more optimistic
about the economy?
H0: pFpUS < 0
HA: pFpUS > 0
Test: Z test
4.
The distributor of the post, a regional newspaper serving
North York is considering three types of dispensing racks.
Management wants to know if the different racks affect
sales. These racks are designated as J-1000, D, and UV-57.
Management also wants to know if the placement of the
racks either inside or outside supermarkets affects sales.
Each of six similar stores was randomly assigned a machine
and location combination, and data were collected on the
number of papers sold over four days.
Ho: no interaction
Ha: interaction
Ho: µj-1000 = µD = µUV57
Ha: at least two means differ
Ho: µinside = µoutside
Ha: at least two means differ
Two-way ANOVA
ERINDA
5.
A pasta chef was experiencing difficulty in getting brands of
pasta to be cooked just right. The main problem she
experiences is with the speed of water absorption by the
different pasta brands. Pasta with a faster rate of water
absorption has a greater tendency to be overcooked. She
decides to conduct an experiment in which two brands of
pasta, one Canadian and one Italian, were cooked for either
4 or 8 minutes. The variable measured was the speed of
water absorption in each case. The results were then
recorded an analyzed.
Ho: no interaction
Ha: interaction
Ho: µc = µI
Ha: at least two means differ
Ho: µ4 = µ8
Ha: at least two means differ
Two-way ANOVA
6.
A large milling machine produces steel rods to certain
specifications. The machine is considered to be running
normally if the standard deviation of the diameter of the rods
is 0.15 millimeters. As line supervisor, you need to test to
see whether the machine is operating normally. You take a
sample of 25 rods and find that the sample standard
deviation is 0.19.
H0: σ2 = 0.0225
HA: σ2 ≠ 0.0225
Test: χ2
7.
Are medical students more motivated than law students? A
randomly selected group of each were administered a
survey of attitudes toward life, which measures motivation
for upward mobility. The scores are summarized below
(higher scores mean greater motivation).
Medical Students Law Students
Sample Size 250 100
Mean Score 83.5 80.2
Pop. Std. Dev. 11.2 9.2
H0: µM − µL < 0
HA: µM − µL > 0
Test: z test
8.
In a recent survey, college students were asked the amount
of time (in hours) they spend weekly watching television and
surfing on the Internet. The researchers were interested in
determining whether the time spent on both activities was
equal. They collected the following data:
Person # 12345678
Internet 2 7 3 8 9 15 7 2
TV 4 15 5 3 4 4 4 8
H0: µd = 0
HA: µd ≠ 0
Test: t test
Part II – True/False (15 marks, 1 mark each) VANESSA
True False
1. In a simple regression model, if the regression model is deemed to be statistically
significant, it means that the regression slope coefficient is significantly greater than
zero
X
2. In a hypothesis test, the p-value measures the probability that the alternative
hypothesis is true.
X
3. If a hypothesis test is conducted for a population mean where only non-negative
values can be sampled, a null and alternative hypothesis of the form: H0 : μ = 100, Ha : μ
100, will result in a one-tailed hypothesis test since the statistic can only assume non-
negative values
X
4. Two variables have a correlation coefficient that is very close to zero. This means
that there is no relationship between the two variables.
X
5. All other things held constant, increasing the level of confidence for a confidence
interval estimate for the difference between two population means will result in a wider
confidence interval estimate.
X
6. The method used in regression analysis for incorporating a categorical variable (no.
of categories = 5) into the model is by organizing the categorical variable into five
dummy variables.
X
7. In a recent one-way ANOVA test, Mean SSW was equal to 1,590 and the Mean SSB
was equal to 310. Therefore, SST is equal to 1,900.
X
8. A local medical center has advertised that the mean wait for services will be less
than 15 minutes (but more than 0 minutes). Given this claim, the hypothesis test for the
population mean should be a one-tailed test with the rejection region in the lower (left-
hand) tail of the sampling distribution.
X
9. Consider the following regression equation: ŷ = 356 + 18.0x1 – 2.5x2. The x1 variable
is a quantitative variable and the x2 variable is a dummy with values 1 and 0. Given this,
we can interpret the slope coefficient on variable x2 as follows: holding x1 constant, if the
value of x2 is changed from 1 to 0, the average value of y will increase by 2.5 units.
X
10. The coefficient of determination measures the percentage of variation in the
independent variable that is explained by the dependent variables in the model.
X
11. A perfect correlation between two variables will always produce a correlation
coefficient of +1.0.
X
12. The prediction interval developed from a simple linear regression model will be at its
narrowest point when the value of x used to predict y is equal to the mean value of x.
X
13. When testing a hypothesis about the variability of a population, the statistical
requirements call for us to convert the variance to standard deviation and run a chi-
square test
X
14. When the expected cell frequencies are smaller than 30, the cells should be
combined in a meaningful way such that the expected cell frequencies do exceed 30.
X
15. If it is known that a simple linear regression model explains 56 percent of the
variation in the dependent variable and that the slope on the regression equation is
negative, then we also know that the correlation between x and y is approximately (-
0.75)
X
16. In estimating the difference between two population means, if a 95 percent
confidence interval includes zero, than we can conclude that there is a 95 percent
chance that the difference between the two population means is zero.
X
17. In a multiple regression analysis, even if only some of the independent variables
have values equal to zero, the regression intercept, b0, can still be meaningful.
X

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Description
Part IProblem Recognition 24 marks 3 marks each2 for hypotheses 1 for testALEXA ski company in Whistler owns two ski shops one near H mm00wBWhistler and one near Blackcomb The following data were collected from both stores Whistler Blackcomb shopshopH mm0AwBMean sales3284351Sample std Dev104151Sample size35 days30 daysTest t testNot equal varianceThe company would like to test for a difference in daily average goggle sales between the two storesH m370000The state lottery office claims that the average household income of those people playing the lottery is greater than H m3700037000 They also know that the distribution of these Ahouseholds income is normal with a standard deviation of 25756 To test their claim a sample of 25 households was studied It was found that the average income in the sample was 36243Test Z testH pp 00FUS In random samples of 1000 people in the United States and in France 70 of the people in the Unites States and 75 H pp 0AFUS of the people in France indicated that they were positive 3about the future economy Does this provide strong evidence that the people in France are more optimistic about the economyTest Z testThe distributor of the post a regional newspaper serving Ho no interactionNorth York is considering three types of dispensing racks Ha interactionManagement wants to know if the different racks affect Ho mm mj1000D UV57sales These racks are designated as J1000 D and UV57 Ha at least two means differManagement also wants to know if the placement of the 4Ho mminsideoutsideracks either inside or outside supermarkets affects sales Ha at least two means differEach of six similar stores was randomly assigned a machine and location combination and data were collected on the number of papers sold over four daysTwoway ANOVA
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