# Devry Math533 week 8 Final Exam Latest 2015 November

August 31, 2017

Question
Devry Math533 week 8 Final Exam Latest 2015 November

1.

Question :

(TCO A)Consider the following raw data that is the result of selecting a random sample of 15 days noting the number of claims an experienced insurance claims adjuster made each day.
31 27 25 26 29
31 25 25 26 21
40 41 31 28 42

a. Compute the mean, median, mode, and standard deviation, Q1, Q3, Min, and Maxfor the above sample data on number of claims per day.
b. In the context of this situation, interpret the Median, Q1, and Q3.

Question 2.

Question :

(TCO B) Consider the following data on customers at an office supply store. These customers are categorized by their previous volume purchases and their age.
20’s

30’s

40’s

50 or older

Total

New Customer

513

285

1,228

100

2,126

Low Volume

417

139

2,578

215

3,349

Mid Volume

250

451

7,859

801

9,361

High Volume

100

615

6,525

994

8,234

Total

1,280

1,490

18,190

2,110

23,070

If you choose one customer at random, then find the probability that the customer

a. is a new customer.
b. is a high volume customer and is in the 40’s.
c. is in the 20’s, given that the customer is low volume.

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Question 3.

Question :

(TCO B) Records of a health insurance company show that 40% of policyholders under age 30 submitted a claim during the past year. A random sample of 75 policyholders under age 30 is selected. Assuming the records are correct, then find the probability that

a. exactly 30 submitted a claim during the past year.
b. more than 32 submitted a claim during the past year.
c. at most 29 submitted a claim during the past year.

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Question 4.

Question :

(TCO B) The demand for gasoline at a local service station is normally distributed with a mean of 27,009 gallons per day and a standard deviation of 4,530 gallons per day.

a. Find the probability that the demand for gasoline exceeds 22,000 gallons for a given day.
b. Find the probability that the demand for gasoline falls between 20,000 and 23,000 gallons for a given day.
c. How many gallons of gasoline should be on hand at the beginning of each day so that we can meet the demand 90% of the time (i.e., the station stands a 10% chance of running out of gasoline for that day)?

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Question 5.

Question :

(TCO C) The Acton Paper Company employs a human resources manager who is given responsibility for employee benefits. There is a question about the mean annual dental expense per employee. The manager selects a random sample of 40 employee records for the past year and finds the following results.

Sample Size = 40
Sample Mean = \$563
Sample Standard Deviation = \$78

a. Construct a 90% confidence interval for the mean annual dental expense per employee.
b. Interpret this interval.
c. How large a sample size will need to be selected if we wish to have a 95% confidence interval with a margin for error of \$10?

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Question 6.

Question :

(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?

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Question 7.

Question :

(TCO D) An article about women in business claims that 28% of all small businesses in the United States are owned by women. Sally Parks believes that this figure is overstated. A random sample of 2,000 small businesses is selected with 546 being owned by women. Does the sample data provide evidence to conclude that less than 28% of small businesses in the United States are owned by women (witha= .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 evidence to conclude that less than 28% of small businesses in the United States are owned by women (witha= .10)?

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Question 8.

Question :

(TCO D) Engineering studies show that it is feasible to install a windmill for generating electrical power if the mean wind speed is greater than 14 mi per hour (mph). The Piedmont Electric Co-op is considering locating mulls at the top of Mount Hunter. A random sample of 45 wind speed readings yields the following results.

Sample Size = 45
Sample Mean = 14.9 mph
Sample Standard Deviation = 3.8 mph

Does the sample data provide sufficient evidence to conclude that installation is feasible at this location (usinga= .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 conclude that installation is feasible at this location (usinga= .10)?

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1.

Question :

(TCO E) Management at New England Life wants to establish the relationship between the number of sales calls made each week (CALLS, X) and the number of sales made each week (SALES, Y). A random sample of 18 life insurance salespeople were surveyed yielding the data found below.
CALLS

SALES

PREDICT

57

18

50

18

2

100

61

18

48

14

58

17

48

13

29

9

43

12

51

17

32

12

59

21

32

8

39

12

54

16

37

9

21

5

62

18

44

14

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Correlations: CALLS, SALES

Pearson correlation of CALLS and SALES = 0.956
P-Value = 0.000

Regression Analysis: SALES versus CALLS

The regression equation is
SALES = – 2.39 + 0.351 CALLS

Predictor Coef SE Coef T P
Constant -2.392 1.231 -1.94 0.070
CALLS 0.35063 0.02674 13.11 0.000

S = 1.50743 R-Sq = 91.5% R-Sq(adj) = 91.0%

Analysis of Variance

Source DF SS MS F P
Regression 1 390.59 390.59 171.89 0.000
Residual Error 16 36.36 2.27
Total 17 426.94

Predicted Values for New Observations

New Obs Fit SE Fit 95% CI 95% PI
1 15.140 0.389 (14.315, 15.965) (11.839, 18.440)
2 32.672 1.538 (29.412, 35.932) (28.107, 37.237)XX

XX denotes a point that is an extreme outlier in the predictors.

Values of Predictors for New Observations

New Obs CALLS
1 50
2 100

a. Analyze the above output to determine the regression equation.
b. Find and interpretβ^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 (a= .05) that the number of calls can be used to predict the sales? 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 sales for all weeks having 50 calls. Interpret this interval.
g. Find the 95% prediction interval for the sales for 1 week having 50 calls. Interpret this interval.
h. What can we say about the sales when we had 100 calls in a week?

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1.

Question :

(TCO E) Southern Textiles Inc. wishes to predict employee wages by using employee’s experience (months of service) and the employee’s education (0=no college degree, 1=college degree). A sample of 20 employees is selected at random.

Y = WAGES (in \$1,000s)
X1= EXP (experience in months)
X2= EDUC (dummy variable 0=no college, 1=college)

The data is given below (in MINITAB).

WAGES

EXP

EDUC

PEXP

PEDUC

37.1

47

1

48

1

30.1

40

0

48

0

35.1

37

1

32.3

45

0

35.2

42

1

37.4

46

1

23.8

17

1

21.0

29

0

32.4

31

1

40.3

60

0

38.5

48

1

36.7

55

0

31.9

43

0

32.1

47

0

28.7

40

0

31.8

37

1

21.8

20

0

24.1

31

0

33.1

37

1

40.8

50

1

Correlations: WAGES, EXP, EDUC

WAGES EXP
EXP 0.851
0.000

EDUC 0.403 -0.086
0.078 0.719

Cell Contents: Pearson correlation
P-Value

Regression Analysis: WAGES versus EXP, EDUC

The regression equation is
WAGES = 9.94 + 0.487 EXP + 5.50 EDUC.

Predictor Coef SE Coef T P
Constant 9.938 1.263 7.87 0.000
EXP 0.48688 0.02897 16.80 0.000
EDUC 5.4964 0.6077 9.04 0.000

S = 1.35387 R-Sq = 95.2% R-Sq(adj) = 94.7%

Analysis of Variance

Source DF SS MS F P
Regression 2 624.36 312.18 170.31 0.000
Residual Error 17 31.16 1.83
Total 19 655.52

Predicted Values for New Observations

New Obs Fit SE Fit 95% CI 95% PI
1 38.805 0.498 (37.753, 39.856) (35.761, 41.848)
2 33.308 0.474 (32.309, 34.308) (30.282, 36.334)

Values of Predictors for New Observations

New Obs EXP EDUC
1 48.0 1.00
2 48.0 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 t-testsonβ^1,β^2(use two tailed test with (a= .05). Interpret your results.
d. Predict the wage for an individual having 48 months of experience and a college degree. Use both a point estimate and the appropriate interval estimate.

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