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Class Times (Circle yours): 9:30 – 10:20     1:30 – 2:20     2:30 – 3:20

STAT 350 Exam 2
Spring 2012

You may have ONLY one sheet of paper with notes handwritten in
your own handwriting to take this test. *1 SHOW ALL YOUR
NECESSARY WORK to receive credit. You MUST write the correct
letter ON THE LINE for EACH multiple choice question. When
you finish your exam, turn it in to your instructor, sign the roster, and

You are expected to uphold the Honor Code of Purdue University. It
is your responsibility to keep your work covered at all times, you
must not exchange anything during the exam. *2

*1 and 2: A grade of 0 will be given, as a punishment to any
violations.

All multiple choice questions are worth 4 points each.

Page        2        3       4         5        6      Cheat-Sheet Total
Points       20      24       16       20       19          1       100
Score

VERSION A
_______ 1.The Arkansas State Police wish to estimate the average mph being traveled on the Interstate
Highways, which cross the state. If the estimate is to be within 8 mpg of the true mean with 98%
confidence and the estimated standard deviation is 24 mph, how large a sample size must be taken?

A. 42               B. 49            C. 15                D. 14                E. 41

_______ 2. A random sample of 100 observations has 25 successes. A 90% confidence interval for p, the
population proportion of success is

A)   .179 and .321
B)   .246 and .254
C)   .248 and .252
D)   .423 and .567
E)   None of the above answers are correct.

_______ 3. Purdue and IUPUI students are asked if they stay up all night before exams. 32% of Purdue
students admitted they have done so, and 29% of IUPUI student said they have done so. A 95%
confidence interval for p1 – p 2 yields 0.03 ± 0.023. If we conducted a significance test of
H0: p1 = p 2 vs. Hα: p 1 ≠ p 2 with α = 0.05, we should (1: Purdue, 2: IUPUI)

A. Reject H0       B. Fail to Reject H0    C. Reject Ha    D. Fail to reject Ha      E. None of A to D.

_______ 4. Which of the following is not typical ANOVA applications?
A) Will three different levels of a chemical concentration have different effects on an electroplating
process?
B) Do four different brands of gasoline have different effects on automobile fuel efficiency?
C) Is there any difference in crop yields when five different fertilizers are used?
D) All of the above.
E) None of the Above.

_______ 5. In a single-factor ANOVA problem involving five populations, which of the following statements are
A) All five population means are equal.
B) All five population means are different.
C) At least two of the population means are different.
D) At least three of the population means are different.
E) At most, two of the population means are equal.
For question #6-#11 (4 pts each), in each of the two boxes, specify which type of problem it is and identify whether
the distribution is a Z, t or F.
For the type of story, it can be any of the following (specify by the letter): May be used more than once.

A. 1-sample mean                           B. 2-sample comparison       C. Matched pair Data
of means
D. 1-sample Proportion                     E. 2-Sample                  F. One-Way ANOVA
Proportion(s)

Type of Story          Distribution
( Z, t, or F )
6. Are there more percentage of vegans in New York than in
California? Suppose if we compare samples of 100 people from
each state?

7. Is there a difference in the average number of green M&Ms
for plain, peanut and almond M&Ms?

8. A report from the M&M/Mars candy company claims that
there is an average of 5 brown M&Ms in each fun pack. Does
our sample of 20 fun packs agree with this?

9. Will a change in the production process will result in
a reduced defective rate? Previous report claimed that
5% of items produced by a manufacturer during a
certain period were defective. An engineer use a sample
of 1000 items by the manufacturer to test this statement.

10. Do vegans in the population consume less than 2000
calories a day on average? We use a sample of 100 people to
test this claim.

11. Each pack has both brown plain M&Ms and brown peanut
M&Ms. 15 packs are randomly selected, for each Joey
counts the numbers of both brown plain M&Ms and brown
peanut M&Ms. He wants to know: On average, are there a
larger number of brown plain M&Ms than brown peanut
M&Ms in the fun packs?

12. Suppose that the two-sided large sample confidence interval for a population mean  at the 95% confidence
level based on a particular sample is (104.6, 109.4). Consider now using this sample to test, at a significance
level of .05, the null hypothesis H o :   110 against the two-sided alternative H a :   110 . Then the p-value
must be _______ .05, so that H o ______ rejected.
A. >, is
B. >, isn’t
C. <, is
D. <, isn’t
accompanying data on breaking load (kg/25 mm width) for various fabrics in both an unabraded condition and an
Fabric

1        2        3         4         5         6        7         8
U        25.6     48.8    49.8      43.2      38.7      55.0      36.4     51.5
B        26.5     52.5    46.5      36.5      34.5      20.0      28.5     46.0
d= U-B     -0.9     -3.7     3.3       6.7       4.2      35.0       7.9      5.5

_______ 13.   What is an appropriate alternative hypothesis for this situation? Suppose d = Unbraded – Braded.

A. d  0
B. d  0 .
C. d  0

A.   One-Sample Mean test
B.   Two-Sample Mean test
C.   Matched-Pair Data’s Mean test
D.   One-Way ANOVA
E.   None of the above.

_______ 15.         Given d  7.25, sd  11.8628 , what is the conclusion to the test in question #13?

A. There is not enough evidence to say that the unbraded condition leads to higher breaking
C. There is not enough evidence to claim that the breaking load for the two fabric conditions
D. There is sufficient evidence to claim that the breaking load for the two fabric conditions

16. When exposed to 100 pCi/L of radon, the radon detector readings are normally distributed. A sample of 12
radon detectors of a certain type was selected (with each exposed to 100 pCi/L of radon) and had a sample
average reading of 97.075 with a sample standard deviation of 6.1095.

a) (4 pts) Based on above data, construct a 95% confidence interval for the population mean reading.
b) (3 pts) Does this data suggest that the population mean reading under these conditions differs from 100?
State the appropriate hypotheses.

c) (3 pts) Calculate the test statistic.

d) (3 pts) Find the p-value.

e) (4 pts) Do you reject H0 or fail to reject H0? Assume  =.05. Also, state the conclusion in layman's terms.

f) (3 pts) Briefly interpret how you could answer part e) using your calculated confidence interval in part a),
instead of the test and P-value in parts c) & d).

17. Are there equal numbers of the different colors of M&Ms in a package? Data was collected to study this
question. Use the outputs below to answer the following questions:

The MEANS Procedure
Color   N      Mean     Std Dev
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
Brown    275     74.748   30.8780
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
Yellow 329       88.588   41.1042
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
Red     327     79.135   32.4722
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
Blue   405     116.338   50.6202
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
Orange 564       144.889   56.3664
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
Green   337     94.246   42.6666
Ƒ ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ

Analysis of Variance
Sum of                Mean
Source               DF              Squares               Square                  F Value

Model               ______           1667491.213            __________             _______
Error               2231             ___________            855.731
Corrected Total    ______            ___________

a) (2 pts)What is the factor(s) in this study? How many levels does the factor(s) have?

b) (4 pts)What are the appropriate (both the null and alternative hypotheses) hypotheses for your test?

c) (9 pts) Complete the above ANOVA table by filling the six missing values. Write them on the above lines.

d) (4 pts) Regardless of the answer to part (b), What is the test statistic value (keep 3 decimal places)? Do you
reject H0 or fail to reject it? Summarize you conclusion in Layman’s terms.

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