Project #52474 - Math533 Finals

Week 8 : Final Exam - Final Exam



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Page 1 


Question 1.1. (TCO A) An insurance company researcher conducted a survey on the number of car thefts in a large city for a period of 20 days last summer. The results are as follows.
            

52              62              51              50              69
58              77              66              53              57
75              56              55              67              73
59              59              68              65              72

 
a. Compute the meanmedianmode, and standard deviation, Q1, Q3, Min, and Max for the above sample data on number of car thefts.
b. In the context of this situation, interpret the Median, Q1, and Q3. (Points : 33)

      
      

 

Question 2.2. (TCO B) Consider the following data on new customers for AJ Auto Insurance, specifically the information of the risk level of the customer and the number of tickets they have had in the last year.

 

0

1

2 or more

Total

Low Risk

56

22

8

86

Medium Risk

18

40

12

70

High Risk

11

13

20

44

Total

85

75

40

200

 
If you choose a customer at random, then find the probability that the customer is
 
a. low risk.
b. low risk and had two or more tickets in the last year.
c. medium risk, given that the customer had zero tickets in the last year. (Points : 18)

      
      

 

Question 3.3. (TCO B) A sales representative for Zavos Air Conditioning Company makes 12 house calls a day. Historically, the probability of making a sale is 12%. On a given day, find the probability that the sales representative makes
 
a. fewer than two sales.
b. exactly two sales.
c. at least two sales. (Points : 18)

      
      

 

Question 4.4. (TCO B) CJ Computer Disks stocks and sells recordable CDs. The monthly demand for these CDs is closely approximated by a normal distribution with a mean of 20,000 disks and standard deviation of 4,000 disks. CJ receives shipments from the supplier once per month (at the beginning of each month).
 
a. Find the probability that the demand for recordable CDs exceeds 30,000 for a particular month. 
b. Find the probability that the demand for recordable CDs is between 12,000 and 18,000.
c. How large an inventory must CJ have available at the beginning of the month so that the probability of running out of recordable CDs (a stock out) during the month is no more than .05? (Points : 18)

      
      

 

Question 5.5. (TCO C) An experiment has been conducted to evaluate a new process for producing synthetic diamonds. Six diamonds have been generated by the new process with recorded weights noted. This yields the following results.
 
Sample Size = 6
Sample Mean = .53 carats
Sample Standard Deviation = .0559 carats

a. Construct the 95% confidence interval for the population mean weight of synthetic diamonds (in carats) using this new synthetic process. 
b. Interpret this interval.
c. How many diamonds should be tested if we wish to generate a 95% confidence interval for the mean weight of synthetic diamonds that is accurate to within .01 carats? (Points : 18)

      
      

 

Question 6.6. (TCO C) A company contemplating the introduction of a new product wants to estimate the percentage of the market that this new product might capture. In a survey, a random sample of 100 potential customers were asked whether they would purchase this new product. The results were that 14 responded affirmatively.
 
a. Compute the 95% confidence interval for the population proportion of potential customers that would purchase the new product.
b. Interpret this confidence interval.
c. How many potential customers should be sampled in order to be 95% confident of being within 1% of the population proportion of potential customers that would purchase the new product? (Points : 18)

      
      

 

Question 7.7. (TCO D) For the past several years, at least 4% of the rooms were not cleaned by room service at the Holton Hotel by 3 p.m. Customer satisfaction surveys have indicated that room availability before 3 p.m. would be a big plus for the hotel. Recently, the executive director took steps to reduce the proportion of rooms not cleaned by 3 p.m. A random sample of 1,400 rooms were selected over a 1-month period and 46 were found not cleaned by 3 p.m. Does the sample data provide evidence to conclude that the percentage of not cleaned rooms by 3 p.m. is less than 4% (with = .05)? Use the hypothesis testing procedure outlined below.
 
a. Formulate the null and alternative hypotheses. 
b. State the level of significance.
c. Find the critical value (or values), and clearly show the rejection and nonrejection regions.
d. Compute the test statistic.
e. Decide whether you can reject Ho and accept Ha or not.
f. Explain and interpret your conclusion in part e.  What does this mean?
g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean?
h. Does the sample data provide evidence to conclude that the percentage of not cleaned rooms by 3 p.m. is less than 4% (with 
= .05)? (Points : 24)

      
      

 

Question 8.8. (TCO D) Carleton Chemical claims that they can produce more than 800 tons of meladone on average per week. A random sample of 36 weeks of production yields the following results.
 
Sample Size = 36
Sample Mean = 823
Sample Standard Deviation = 79.8
 
Does the sample data provide sufficient evidence to support the claim made by Carleton Chemical (using 
a = .10)? Use the hypothesis testing procedure outlined below.
 
a. Formulate the null and alternative hypotheses. 
b. State the level of significance.
c. Find the critical value (or values), and clearly show the rejection and nonrejection regions.
d. Compute the test statistic.
e. Decide whether you can reject Ho and accept Ha or not.
f. Explain and interpret your conclusion in part e. What does this mean?
g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean?
h. Does the sample data provide sufficient evidence to support the claim made by Carleton Chemical (using 
a = .10)? (Points : 24)

      
      

 

Week 8 : Final Exam - Final Exam



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Page 2 

Question 1.1. (TCO E) A specialist in hospital administration stated that the number of FTEs (full-time employees) needed in a hospital can be estimated by counting the number of beds in the hospital (a common measure of hospital size). A researcher decided to develop a regression model in an attempt to predict the number of FTEs (Y) of a hospital by the number of beds (X). She surveyed 17 small hospitals and obtained the following data with the following Minitab printout.
 

BEDS

FTE

PREDICT

23

69

65

29

95

100

29

102

 

30

98

 

35

118

 

40

120

 

42

126

 

46

125

 

50

142

 

50

138

 

54

178

 

60

165

 

64

156

 

66

184

 

70

187

 

76

176

 

78

225

 



 
 
Correlations: BEDS, FTE 
 
Pearson correlation of BEDS and FTE = 0.953
P-Value = 0.000

 
Regression Analysis: FTE versus BEDS 
 
The regression equation is
FTE = 30.9 + 2.23 BEDS.
 
 
Predictor     Coef  SE Coef       T      P
Constant    30.904    9.611    3.22  0.006
BEDS        2.2312   0.1837   12.15  0.000
 
 
S = 12.7783   R-Sq = 90.8%   R-Sq(adj) = 90.2%
 
 
Analysis of Variance
 
Source          DF      SS      MS       F      P
Regression       1   24095   24095  147.56  0.000
Residual Error  15    2449     163
Total           16   26544
 
 
Predicted Values for New Observations
 
New Obs      Fit  SE Fit       95% CI            95% PI
      1   175.93   4.20   (166.97, 184.89)  (147.26, 204.60)
      2   254.02   9.77   (233.19, 274.85)  (219.73, 288.31)X
 
X denotes a point that is an extreme outlier in the predictors.
 
 
Values of Predictors for New Observations
 
New Obs  BEDS
      1    65
      2   100
 
a. Analyze the above output to determine the regression equation.
b.Find and interpret 
βË–1in the context of this problem.
c. Find and interpret the coefficient of determination (r-squared).
d. Find and interpret coefficient of correlation. 
e. Does the data provide significant evidence (
= .05) that beds can be used to predict FTEs? Test the utility of this model using a two-tailed test. Find the observed p-value and interpret.
f. Find the 95% confidence interval for mean FTEs over all hospitals that have 65 beds. Interpret this interval.
g. Find the 95% prediction interval for the FTEs for a hospital that has 65 beds. Interpret this interval.
h. What can we say about the FTEs when the hospital has 100 beds? (Points : 48)

      
      

 

Week 8 : Final Exam - Final Exam



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4 

Question 1.1. (TCO E) Holding goods in inventory is costly because inventoried goods are susceptible to breakage and other forms of physical damage. Typically, the amount of damage increases with the level of inventory, but some of the damage is unrelated to the amount of inventory. In addition, the seasonality may make a difference. A random sample of 10 observations is selected with the variables INVTRY (X1, inventory in $1,000,000s), SEASON (X2, with spring and summer being 0 and fall and winter being 1), and DAMAGE (Y, in $10,000s). The results are found below.
 

INVTRY

SEASON

DAMAGE

11

1

80

15

1

100

13

0

70

10

1

60

7

0

50

9

0

70

13

1

100

10

0

65

14

1

95

8

0

54

15

0

96

9

1

91

13

1

85

 
 
Correlations: INVTRY, SEASON, DAMAGE 
 
        INVTRY   SEASON
SEASON   0.349
         0.242
 
DAMAGE   0.798    0.578
         0.001    0.038
 
 
Cell Contents: Pearson correlation
               P-Value
 
 
Regression Analysis: DAMAGE versus INVTRY, SEASON 
 
The regression equation is
DAMAGE = 21.2 + 4.49 INVTRY + 11.7 SEASON.
 
 
Predictor    Coef  SE Coef     T      P
Constant    21.16    12.44  1.70  0.120
INVTRY      4.485    1.138  3.94  0.003
SEASON     11.670    5.896  1.98  0.076
 
 
S = 9.93147   R-Sq = 73.9%   R-Sq(adj) = 68.7%
 
 
Analysis of Variance
 
Source          DF      SS      MS      F      P
Regression       2  2797.4  1398.7  14.18  0.001
Residual Error  10   986.3    98.6
Total           12  3783.7
 
 
Predicted Values for New Observations
 
New Obs    Fit  SE Fit      95% CI           95% PI
      1  86.65    3.76  (78.27, 95.02)  (62.99, 110.30)
 
 
Values of Predictors for New Observations
 
New Obs   INVTRY  SEASON
      1     12.0    1.00
 
 
a. Analyze the above output to determine the multiple regression equation.
b. Find and interpret the multiple index of determination (R-Sq). 
c. Perform the multiple regression t-tests on 
βË–1βË–2 (use two tailed test with (= .10). Interpret your results.
d. Predict the damage for a single case in the spring or summer with an inventory of $12,000,000. Use both a point estimate and the appropriate interval estimate. (Points : 31)

      
      

 

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Subject Mathematics
Due By (Pacific Time) 12/18/2014 11:59 pm
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