Description

Stat 1 Sec. 6&12

T-H Final

Name _______________

Show & Justify Your Work

Label & Scale Axes

Dr. Etterbeek

Fall Ã¢â‚¬Ëœ21

Ã¢Ë†â€˜=

1. When bears were anesthetized, researchers measured the diameter (in inches) of the

bearsÃ¢â‚¬â„¢ chests and weighed the bears (in pounds). The results are shown in the table

below.

x Chest (in)

26

45

54

49

41

49

44

19

y Weight (lb)

90

304

446

348

321

395

259

58

yÃŒâ€š

RESID

(14)

a. Find the regression equation for yÃŒâ€š in terms of x.

b. Identify the predictor and response variables and give their dimensions.

c. Find and interpret the slope of the regression line in context.

d. Graph the observations and the regression line.

1

1. (cont.)

e. Use your graph to estimate the weight of a bear with a chest size of 40 inches.

(Show your work.)

f. Use the regression equation to estimate the weight of a bear with a chest size

of 40 inches. (Show your work.)

g. Complete the table giving the estimated weight and the residuals.

h. Find the correlation coefficient.

i. Graph the residuals.

j. Use the results of parts (h) and (i) to determine the appropriateness of a linear

model for these data.

2

2. The urn contains 1 ball numbered one, 2 balls numbered two , 3 balls numbered

three, and 4 balls numbered four as shown in the figure below.

1

2

2

3

3

4

4

4

3

4

A ball is drawn at random from the urn, and the random variable X equals the number

on the ball.

(6)

a. Complete the frequency table for the random variable X .

x

Frequency

b. Complete the probability table for the random variable X .

x

Pr(x)

xPr x

()

x Pr ( x )

2

c. Find and interpret the mean of X. (Show your work.)

d. Find the standard deviation of X. (Show your work.)

3

3. The data in the table below gives the daily costs of 15 randomly selected families of

four to spend one day at an American amusement park.

256

221

209

212

178

195

218

208

207

189

152

179

172

184

181

In this problem you will be computing a confidence interval for the average cost of a

family of four to spend one day at an American amusement park. You may assume

that the daily costs for all families of four at an amusement park are normally

distributed.

(10)

a. For this situation define the:

Population X:

Estimated Parameter:

Estimator:

Population X :

b. Construct a 99% confidence interval for the population mean.

i. Interval and Conditions

Interval:

Conditions:

4

3. (cont.)

ii. Computation:

iii. Interpretation

Confidence Interval:

Confidence Level:

4. The data shown in the table below gives the total weights of garbage (in pounds) for

one week for 32 randomly selected households in the Providence area. It is known

that the standard deviation for all of the weekly weight of garbage in the Providence

area is 8.4 lbs

10.76

19.98

27.60

38.11

27.90

21.90

21.83

14.95

33.27

35.54

44.44

45.17

33.07

10.35

44.44

24.13

37.60

38.96

17.17

31.60

22.22

42.99

20.20

36.80

19.02

15.43

20.71

17.01

23.67

19.13

20.99

21.18

In this problem you will be testing an hypothesis concerning the average weekly

weight of household garbage (in pounds) in the Providence area. Ã¢Ë†â€˜ x = 858.12 )

(10)

a. For this situation define the:

Population X:

Hypothesized Parameter:

Estimator:

Population X :

5

4. (cont.)

b. Can we conclude at the 0.05 level of significance that the mean weight of

household garbage for one week in the Providence area is different

from 30 lb

i. Hypotheses:

H0:

Ha:

ii. Conditions:

iii. Computation:

0

iv. Conclusion:

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Table of t distribution.

7

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