ECONOMICS 601-Home Texas San Antonio final exam

| August 30, 2017

Question

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.

3.1 4.2 2.0 3.5 2.6
5.3 3.5 3.1 2.6 3.3
4.7 3.7 3.0 2.6 4.0
3.8 4.4 3.2 3.2 3.8

a. Compute the mean, median, mode, and standard deviation, Q1, Q3, Min, and Maxfor 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) JR Trucking buys tires from three suppliers: Goodyear, Michelin, and Bridgestone. Data on the last 1,000 tires that were purchased are described in the table below.

Defective

Not Defective

Total

Goodyear

5

495

500

Michelin

6

294

300

Bridgestone

10

190

200

Total

21

979

1000

If you choose a tire at random, then find the probability that the tire

a. was made by Michelin.
b. was made by Goodyear and was defective.
c. was not defective, given that the tire was made by Bridgestone. (Points : 18)

Question 4.4.(TCO B) Telcom is a telephone answering service for physicians. The length of a message is a normally distributed variable with a mean 152.3 seconds and a standard deviation of 22.8 seconds.

a. What percentage of messages lasts longer than 120 seconds?
b. What percentage of messages lasts between 90 and 120 seconds?
c. Find the 95th percentile for length of message (i.e., find the cutoff for the longest 5% of messages). (Points : 18)

.

.
b. Interpret this interval.

c. How large a sample size will need to be selected if we wish to have a 99% confidence interval with a margin for error of .10 oz? (Points : 18)

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Question 6.6.(TCO C) The manufacturer of a certain brand of toothpaste claims that a high percentage of dentists recommend the use of their toothpaste. A random sample of 400 dentists results in 310 recommending their toothpaste.

a. Compute the 99% confidence interval for the population proportion of dentists who recommend the use of this toothpaste.

b. Interpret this confidence interval.

.

c. How large a sample size will need to be selected if we wish to have a 99% confidence interval that is accurate to within 3%? (Points : 18)

Question 8.8.(TCO D) A restaurant franchise company has a policy of opening new restaurants only in areas that have a mean household income in excess of $65,000. The company is currently considering an area to open a new restaurant. A random sample of 144 households from this area is selected yielding the following results.

Sample Size = 144
Sample Mean = $66,124
Sample Standard Deviation = $7,400

Does the sample data provide evidence to conclude that the population mean annual household income is in excess of $65,000 (usinga= .05)? Use the hypothesis testing procedure outlined below.

a. Formulate the null and alternative hypotheses.

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 population mean annual household income is in excess of $65,000 (usinga= .05)? (Points : 24)

Question 9.(TCO E) At an auction, a national car rental agency sold 12 comparably equipped 3-year-old Chevrolet Corsicas. The data on mileage (X) and selling price (Y) are found below.

PRICE

MILEAGE

PREDICT

7000

60000

54000

8500

52000

80000

7000

62000

8900

48000

7600

55000

7200

60000

8500

50000

7800

53000

7200

58000

9000

48000

7200

60000

7700

55000

Correlations: PRICE, Mileage

Pearson correlation of PRICE and Mileage = -0.970
P-Value = 0.000

Regression Analysis: PRICE versus Mileage

The regression equation is
PRICE = 15809 – 0.145 Mileage

Predictor Coef SE Coef T P
Constant 15809.0 635.2 24.89 0.000
Mileage -0.14540 0.01149 -12.66 0.000

S = 188.396 R-Sq = 94.1% R-Sq(adj) = 93.5%

Analysis of Variance

Source DF SS MS F P
Regression 1 5685070 5685070 160.17 0.000
Residual Error 10 354930 35493
Total 11 6040000

Predicted Values for New Observations

New Obs Fit SE Fit 95% CI 95% PI
1 7957.5 55.8 (7833.2, 8081.8) (7519.7, 8395.3)
2 4177.2 291.4 (3527.9, 4826.4) (3404.1, 4950.3)XX

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

Values of Predictors for New Observations

New Obs Mileage
1 54000
2 80000

a. Analyze the above output to determine the regression equation.

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b. Find and interpret??1in the context of this problem.

.

c. Find and interpret the coefficient of determination (r-squared).

R

d. Find and interpret coefficient of correlation.

e. Does the data provide significant evidence (a= .05) that the mileage can be used to predict the price? 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 price of 3-year-old Chevy Corsicas that have 54,000 in mileage. Interpret this interval.

95% CI 95% PI
(7833.2, 8081.8) (7519.7, 8395.3)

g. Find the 95% prediction interval for the price of a single 3-year-old Chevy Corsica that has 54,000 in mileage. Interpret this interval. .

h. What can we say about the price for a 3-year-old Chevy Corsica that has 80,000 in mileage?

It is an outlier…

95% CI 95% PI

(3527.9, 4826.4) (3404.1, 4950.3)XX

(Points : 48)

Question 10.(TCO E) At an auction, a national car rental agency sold 12 comparably equipped 3-year-old Chevrolet Corsicas. The data on mileage (X1), type of car (X2), and selling price (Y) are found below.

Y = PRICE ($)
X1= MILEAGE (miles)
X2= TYPE (dummy variable 0=sedan, 1=coupe)

The data is given below (in MINITAB).

PRICE

Mileage

Type

PredMile

PredType

7000

60000

0

54000

0

8500

52000

0

54000

1

7000

62000

0

8900

48000

0

7600

55000

0

7200

60000

1

8500

50000

1

7800

53000

1

7200

58000

1

9000

48000

1

7200

60000

1

7700

55000

0

Correlations: PRICE, Mileage, Type
PRICE Mileage
Mileage -0.970
0.000

Type 0.023 -0.053
0.942 0.871

Cell Contents: Pearson correlation
P-Value

Regression Analysis: PRICE versus Mileage, Type

The regression equation is
PRICE = 15841 – 0.146 Mileage – 39 Type.

Predictor Coef SE Coef T P
Constant 15840.9 671.4 23.59 0.000
Mileage -0.14562 0.01205 -12.09 0.000
Type -39.5 114.1 -0.35 0.737

S = 197.278 R-Sq = 94.2% R-Sq(adj) = 92.9%

Analysis of Variance

Source DF SS MS F P
Regression 2 5689732 2844866 73.10 0.000
Residual Error 9 350268 38919
Total 11 6040000

Predicted Values for New Observations

New Obs Fit SE Fit 95% CI 95% PI
1 7977.5 82.1 (7791.7, 8163.3) (7494.1, 8460.9)
2 7938.0 81.2 (7754.4, 8121.6) (7455.4, 8420.6)

Values of Predictors for New Observations

New Obs Mileage Type
1 54000 0.00
2 54000 1.00

a. Analyze the above output to determine the multiple regression equation.

b. Find and interpret the multiple index of determination (R-Sq).

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c. Perform the t-testson??1,??2(use two tailed test with (a= .05). Interpret your results.

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