SMAM 320
Exam #2
Form F
October 24, 2008
Name
1. According to research reported in the Journal of the National Cancer Institute (Apr. 1991), eating foods
high in fiber may help protect against breast cancer. The researchers randomly divided 120 laboratory rats
into four groups of 30 each. All rats were injected with a drug that causes breast cancer, and then each rat
was fed a diet of fat and fiber for 15 weeks. However, the levels of fat and fiber varied from group to
group. At the end of the feeding period, the number of rats with cancer tumors wad determined for each
group. The data are summarize in the following table and are in the Minitab file CancerTumors.mtw.
Tumors
Yes
No
HighFat/NoFiber
27
3
Diet
HighFat/Fiber
20
10
LowFat/NoFiber
19
11
LowFat/Fiber
14
16
Is there evidence that the proportion of rats with tumors is not the same for all four diets compared?
Test the relevant hypotheses using α = .05. You should answer this question by
providing the following information:
a) Give the percentages of the rats that had tumors for each of the diets.
How would you interpret and compare those numbers in context? {3 points}
b) Tell whether this is a test of homogeneity or a test of association. Explain why. {3 points}
c) Identify the null and alternate hypotheses.
H0:
{2 points}
Ha:
{2 points}
SMAM 320
Exam #2
Form F
October 24, 2008
Page 2 of 8
d) Use Minitab to perform the appropriate test. Copy/paste the output in the space provided below.
{3 points}
e) Provide the following information from the Minitab output. . {1, 1, 1, 1, 2 points}
The Expected number of the rats fed the Low-Fat/Fiber diet that had tumor
{1 point}
Value of the test statistic =
df =
{1 point}
P-value =
{1 point}
{1 point}
Your decision
{2 points}
f) Please write your conclusion in the context of this problem. Refer also to part a) in your conclusion.
{3 points}
SMAM 320
Exam #2
Form F
October 24, 2008
Page 3 of 8
2. Management of a company that develops websites was interested in determining which variables have the
greatest impact on the number of websites developed and delivered to customers per quarter. Data were
collected on website production output for 13 three-person website development teams. The data is in the
file: WebdVSTeamExp.mtw.
WebDeliv: Number of websites completed and delivered to customers during the quarter
TeamExp: Number of months team has been together
a) Use Minitab to perform a regression analysis to predict WebDeliv in terms of TeamExp. Copy/Paste the
part of the output before the Analysis of Variance output into the space provided below. {3 points}
b) In your output, there is a line headed by TeamExp. In that line there is a P-value. Please identify the
hypotheses that are associated with that P-value, state the P-value, your decision and provide an
appropriate conclusion in the context of this analysis.
H0:
{2 points}
HA:
{2 points}
{1 point}
P-value =
Decision and conclusion: {3 points}
c) Compute a 95% confidence interval for the true slope, β, associated with this least squares linear model.
Make sure that you identify the correct degrees of freedom and the t* value used in the calculation of the
confidence interval.
df =
t*=
{1 points}
95% Confidence interval =
{2 points}
{2 points}
SMAM 320
Exam #2
Form F
October 24, 2008
Page 4 of 8
d) Write a sentence that gives the value of the coefficient of determination and indicates the meaning of that
coefficient in context. {3 points}
e) Write a sentence that describes how does the WebDeliv, on average, change for each additional
1 month increase in TeamExp. {2 points}
f) Please use this model to calculate both a point estimate and a 95% interval estimate for the
WebDeliv for a team that has 12 months of TeamExp.
Point estimate:
95% interval estimate:
{2 points}
{2 points}
g) Produce a plot of the residuals versus the fits (select Residuals versus fits on Graphs tab).
Copy/paste special as Enhanced Metafile or Bitmap into the space provided below.
{2 points}
Describe the plot and write a conclusion in terms of the assumption made for a Linear
Regression Model checked with this plot {3 points}
SMAM 320
Exam #2
Form F
October 24, 2008
Page 5 of 8
3. The management of the website development company mentioned in the previous problem not only
recorded
WebDeliv: Number of websites completed and delivered to customers during the quarter
TeamExp: Number of months the team has been together but they also recorded the values of a number of
other variables
Backlog: Number of website orders in backlog at the close of the quarter
ProcessChange: A change in the website development process occurred during the period for which the
data was collected: 1 if change had already been made; 0 otherwise
Year: 2001 or 2002
Quarter: 1, 2, 3, or 4
Minitab was used to perform a multilinear regression. The output is given below.
Regression Analysis: WebDeliv versus TeamExp, Backlog, ...
The regression equation is
WebDeliv = - 10885 - 0.404 TeamExp + 0.154 Backlog + 7.45 ProcessChange
+ 5.44 Year + 2.01 Quarter
Predictor
Constant
TeamExp
Backlog
ProcessChange
Year
Quarter
S = 5.07103
Coef
-10885
-0.4035
0.1540
7.451
5.439
2.0100
SE Coef
5389
0.2241
0.1324
2.116
2.693
0.8515
R-Sq = 52.3%
T
-2.02
-1.80
1.16
3.52
2.02
2.36
P
0.047
0.076
0.249
0.001
0.047
0.021
R-Sq(adj) = 48.8%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
5
67
72
SS
1889.95
1722.93
3612.88
MS
377.99
25.72
F
14.70
P
0.000
a) There is an arrow on the output pointing to a P-value. Please give the hypotheses, the P-value, the
decision and write a sentence in the context of the problem that gives your conclusion.
H0:
{2 points}
HA:
{2 points}
P-value =
{1 point}
Decision and conclusion: {3 points}
SMAM 320
Exam #2
Form F
October 24, 2008
b) Which of the variables are significant at the 0.15 level of significance?
Page 6 of 8
{3 points}
c) Write in a sentence on the average, how many more websites would the delivered for each additional
website in the backlog. {2 points}
d) Write a sentence explaining how the occurrence of a change in the website development process
(ProcessChange) affected the WebDeliv on average, if the other variables are all held constant.
{2 points}
f) Write a sentence telling whether or not you would find this model useful in a practical sense for
estimating WebDeliv for this company.
Consider the values R2-Adj and se when making your decision.
{3 points}
SMAM 320
Exam #2
Form F
October 24, 2008
Page 7 of 8
4. You are saving to buy a house or condo and you wonder how much it will cost. Depending on what you
want and its location, the price will vary dramatically. The house selling prices in the Minitab file
HousePrices.MTW has 100 recent home sales in Gainesville, Florida. Variables listed are
Prices (in dollars), Taxes (in dollars), lot size, house size, number of Bedrooms, number of Bathrooms,
NW=1 if Northwest quadrant of town, NW=0 otherwise. NOTE: Northwest quadrant is considered the most
desirable location.
A. Fit a model to predict Prices, using Taxes, lot size, house size and NW region as predictors.
Copy/paste the output (up to Analysis of Variance output) in the space provided below. 3 points
B. Is there evidence that a home located in the NW region affects the selling price? To answer this
question, conduct a test of hypothesis; give the test statistic and the p value. Give your decision and
write a conclusion in context.
3 points
C. Give the value of the regression coefficient of NW, and write a sentence explaining this value in context.
2 points
SMAM 320
Exam #2
Form F
October 24, 2008
Page 8 of 8
5. Acme Toy Company prints baseball cards. The company claims that 30% of the cards are rookies, 60%
veterans, and 10% are All-Stars. The cards are sold in packages of 100.
Suppose a randomly-selected package of cards has 50 rookies, 45 veterans, and 5 All-Stars. Is this
consistent with Acme's claim? Use a 0.05 level of significance.
a) Tell whether this is a test of homogeneity, test of association, or goodness of fit test.
Explain.
2 points
b) Identify the null hypothesis and alternate hypothesis.
1 point each
H0:
Ha:
c) Use Minitab to perform the necessary test. Copy/paste the output below. 2 points
d) Write your decision and conclusion in the context of the problem. If the null hypothesis is
rejected, explain the inconsistency using the Minitab output in part c).
2 points