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Value - Applications of Statistics - Exam Key, Exams of Statistics

Senate of Serampore College (University)Statistics

This is the Exam Key of Applications of Statistics which includes Variable, Researcher, Type of Variable, Observational Unit, Sample Size, Dendritic Branches, Emanating, Humans and Animals, Disease etc. Key important points are: Value, Definition, Central Limit Theorem, Distribution, Sample Mean, Variance, Affect, Moderately, Controlled Experiment, Placebo

Typology: Exams

2012/2013

Uploaded on 02/26/2013

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STAT 205 Name:___ANSWER KEY____________
Fall 2006
Final Exam
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Download Value - Applications of Statistics - Exam Key and more Exams Statistics in PDF only on Docsity!

STAT 205 Name:___ANSWER KEY____________

Fall 2006

Final Exam

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This exam is worth a total of 120 points.

Part I: Answer eight of the following nine questions. If you complete more than eight, I

will grade only the first eight. Five points each.

1) State the definition of a P-value.

The probably under the null hypothesis of observing a test statistic this extreme or more

(in the direction of the alternative hypothesis).

2) The Central Limit Theorem says that for any i.i.d. random sample, Y 1 , Y 2 , …, Yn where

E[Yi ] = μ and E[(Yi - μ)

2

] = σ

2

, then as n→∞ the distribution of the sample mean is

____normal_ with mean, μ__, and variance, __σ

2

/n_____(note, I’m asking for variance

here – not standard deviation).

3) The compound m -chlorophenylpiperazine (mCPP) is thought to affect appetite and food

intake in humans. In a study of the effect of mCPP on weight-loss, eight moderately obese

men were given mCPP in a double-blind, placebo controlled experiment. Some of the men

took mCPP for two weeks, then took nothing for two weeks (a “washout period”), and then

took a placebo for two weeks. The rest of the men took the placebo during the first two

weeks, then had a two week washout period, then took mCPP for the final two weeks. The

The men were asked to rate how hungry they were at the end of each two-week period

(hunger rating for mCPP period – hunger rating for placebo period). A QQplot of the

differences was constructed (below).

(Circle the correct answer.) The use of the independent samples t-test /

dependent samples t-test / sign test / Wilcoxon-Mann-Whitney test would be

appropriate here.

A simple linear regression was performed to relate the cocoon temperature (Y in

o

C) to the outside air temperature (X in

o

C). Use this portion of DoStat’s output to

answer the following 3 questions.

7) What is the r

2

for this regression? __0.9425586_______

8) Interpret the value of the coefficient of determination (r

2

) in the context of the

setting.

94% of the variation in cocoon temperature is explained by the variation in outside

air temperature.

9) Referring to the default test DoStat performs for the β1, fill in the blanks:

H0: ________β 1 = 0____________________________

HA: ________β 1 ≠_0___________________________

P-value: ____<0.0001____________________________

Part II: Answer every part of the next three problems. Read each question

carefully, and show your work for full credit.

1) It is common folk wisdom that drinking cranberry juice can prevent urinary tract

infection in women. In 2001, the British Medical Journal reported the results of a

Finnish study in which two groups of 50 women were monitored for these infections

over 6 months. One group drank cranberry juice every day and the other group did

not drink cranberry juice. At the end of the study, the number of women who had

urinary tract infections (one or more) was 8 for the cranberry juice group and 18 for

the group that did not drink cranberry juice.

1a) (20 points) Construct a 95% Agresti-Caffo confidence interval for the

difference in the proportion of urinary tract infections for these two groups.

Let 1 denote cranberry juice group and 2 denote the group that did not drink

cranberry juice.

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1

p = 50 2

2

p =

2

2 2

1

1 1

2

1 2

n

p p

n

p p p p Z α

Our 95% confidence interval is (-0.359, -0.026)

1b) (5 points) Interpret the interval you just computed in part (a).

We are 95% confident that the proportion of women who get urinary tract infections

is larger for women who do not drink cranberry juice by as little as 0.026 or as much

as 0.359.

3) Twenty plots, each of equal area, were randomly chosen in a large field of corn. For

each plot, the plant density (number of plants in the plot) and the mean cob weight (g

of grain per cob) were observed. The results are given in the table.

Plant Density X Cob Weight Y Plant Density X Cob Weight Y

Preliminary calculations yield the following results:

3a) (7 points) Calculate the least-squares regression line using X=plant density

as the predictor variable and Y=cob weight as the response.

b 1 =

∑

∑

=

=

n

i

i

n

i

i i

x x

x x y y

1

2

1

b 0 = y − b 1 x = 224.1 – (-0.721)(128.05) = 316.

Our line is Y = 316.42 - 0.721X

3b) (7 points) Calculate the residual standard deviation (S Y|X).

n −

SS resid

= 8.619 g

3c) (7 points) Give an estimate of the mean and standard deviation of cob

weight at a plant density of 145.

μˆ^ Y | X = 316. 42 − 0. 721 )( 145 )= 211. 875 g

S Y|X = 8.619 g

3d) (7 points) Calculate a 95% confidence interval for β 1 (slope of the true line).

∑

n

i

i

YX

x x

S

b t

1

2

|

2

1

( )

α

3e) (7 points) Interpret the interval you just computed in part (d).

We are 95% confident that for every one plant of corn increase per plot, we

expect the mean cob weight to decrease by as little as 0.593 or as much as 0.

grams of grain per cob.