# Project #15134 - Tim Mandalay

Week 8 : Final Exam - Final Exam

Top of Form

 Time Remaining: Page:  1

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.              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 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) East Side Bank has three loan officers, Jim, Sally, and Dave, who process all loan applications. Each application results in an approval, rejection, or delay. The results of the last 100 loan applications are shown below.

 Jim Sally Dave Total Approved 20 16 18 54 Rejected 1 7 14 33 Delayed 5 2 6 13 Total 37 25 38 100

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

a. was processed by Jim.
b. was approved and processed by Sally.
c. was rejected, given that the application was processed by Dave. (Points : 18)

 Question 3.3. (TCO B) A sales representative for Zavos Air Conditioning Company makes 20 house calls a day. Historically, the probability of making a sale is 5%. On a given day, find the probability that the sales representative makes   a. at most three sales. b. exactly three sales. c. more than three sales. (Points : 18)

 Question 4.4. (TCO B) At a local supermarket the monthly customer expenditure follows a normal distribution with a mean of $495 and a standard deviation of$121.    a. Find the probability that the monthly customer expenditure is less than $300 for a randomly selected customer. b. Find the probability that the monthly customer expenditure is between$300 and $600 for a randomly selected customer. c. The management of a supermarket wants to adopt a new promotional policy giving a free gift to every customer who spends more than a certain amount per month at this supermarket. Management plans to give free gifts to the top 8% of its customers (in terms of their expenditures). How much must a customer spend in a month to qualify for the free gift? (Points : 18)  Question 5.5. (TCO C) Until this year, the mean braking distance of a Nikton automobile moving at 60 mi per hour was 175 ft. Nikton engineers have developed what they consider a better braking system. They test the new brake system on a random sample of 81 cars and determine the sample mean braking distance. The results are the following. Sample Size = 81 Sample Mean = 167 ft Sample Standard Deviation = 27 ft a. Compute the 95% confidence interval for the mean braking distance. b. Interpret this interval. c. How many cars should be tested if Nikton wants to be 95% confident of being within 2 ft of the population mean braking distance? (Points : 18)  Question 6.6. (TCO C) United Express Delivery is interested in estimating the percentage of packages delivered damaged. A simple random sample of 500 packages yields 12 delivered damaged and 488 delivered undamaged. a. Compute the 99% confidence interval for the population proportion of packages that are delivered damaged. b. Interpret this confidence interval. c. How many packages should be sampled in to order to be 99% confident of being within .5% of the actual population proportion of packages delivered damaged? (Points : 18) Question 7.7. (TCO D) A manager at Travis Savings and Loan believes that less than 52% of their depositors own their homes. A random sample of 100 depositors is selected with the results that 46 depositors own their homes and the other 54 do not own their homes. Does the sample data provide evidence to conclude that less than 52% of all depositors at Travis Savings and Loan own their homes (with a = .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 less than 52% of all depositors at Travis Savings and Loan own their homes (with a = .05)? (Points : 24) Week 8 : Final Exam - Final Exam Top of Form  Time Remaining: Page: 1 2 3 Page 2 Question 1.1. (TCO E) A local realtor wishes to study the relationship between selling price (PRICE in$) and house size (HOUSESIZE in square feet). A sample of 10 homes is selected at random. The data is given below (in MINITAB).

 PRICE HOUSESIZE PREDICT 100000 1600 2000 107000 1750 4000 121000 1900 124000 2150 132000 2400 140000 2300 144000 2400 158000 2700 170000 3000 182000 2900

Correlations: PRICE, HOUSESIZE

Pearson correlation of PRICE and HOUSESIZE = 0.971
P-Value = 0.000

Regression Analysis: PRICE versus HOUSESIZE

The regression equation is
PRICE = 11730 + 54.6 HOUSESIZE

Predictor      Coef  SE Coef       T      P
Constant      11730    11098    1.06  0.321
HOUSESIZE    54.576    4.717   11.57  0.000

S = 6676.82  R-Sq = 94.4%  R-Sq(adj) = 93.7%

Analysis of Variance

Source          DF           SS            MS        F      P
Regression       1   5968960529    5968960529   133.89  0.000
Residual Error   8    356639471      44579934
Total            9   6325600000

Predicted Values for New Observations

New Obs      Fit  SE Fit       95% CI            95% PI
1   120881    2568  (114959, 126804) (104385, 137378)
2   230033    8246  (211018, 249048) (205566, 254500)XX

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

Values of Predictors for New Observations

New Obs HOUSESIZE
1     2000
2     4000

a. Analyze the above output to determine the regression equation.
b. Find and interpret
βˆ1in 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) the house size can be used to predict the selling 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 selling price for homes that are 2000 square feet in size. Interpret this interval.
g. Find the 95% prediction interval for the selling price of a single home that is 2000 square feet in size. Interpret this interval.
h. What can we say about the selling price for a home that is 4,000 sq. ft in size?

(Points : 48)

 Page:  1  2  3 Time Remaining:

Bottom of Form

 Question 8.8. (TCO D) A manufacturer of athletic footwear claims that the mean life of his product will exceed 50 hours. A random sample of 36 shoes leads to the following results in terms of useful life.   Sample Size = 36 shoes Sample Mean = 52.3 hours Sample Standard Deviation = 9.6 hours   Does the sample data provide evidence to conclude that the manufacturer’s claim is correct (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 evidence to conclude that the manufacturer’s claim is correct (using a = .10)? (Points : 24)

 Page:  1 Time Remaining:

Week 8 : Final Exam - Final Exam

Top of Form

 Time Remaining: Page:  1  2  3

4

Question 1.1. (TCO E) A local realtor wishes to study the relationship between selling price (PRICE in \$), house size (HOUSESIZE in square feet), lot size (LOTSIZE in acres), and number of bathrooms (BATHROOM). A sample of 10 homes is selected at random. The data is given below (in MINITAB).

 PRICE HOUSESIZE LOTSIZE BATHROOMS Pred House Size Pred Lot Size Pred Bath 100000 1600 0.8 1.5 2500 1 2.5 107000 1750 0.8 2.0 2500 5 2.5 121000 1900 0.8 2.5 124000 2150 1.0 2.5 132000 2400 0.9 2.5 140000 2300 0.9 3.0 144000 2400 1.0 2.5 158000 2700 1.0 3.0 170000 3000 1.0 3.0 182000 2900 1.2 3.5

Correlations: PRICE, HOUSESIZE, LOTSIZE, BATHROOMS

PRICE     HOUSESIZE     LOTSIZE
HOUSESIZE     0.971
0.000

LOTSIZE       0.919       0.875
0.000       0.001

BATHROOMS     0.921       0.877        0.877
0.000       0.001        0.002

Cell Contents: Pearson correlation
P-Value

Regression Analysis: PRICE versus HOUSESIZE, LOTSIZE, BATHROOMS

The regression equation is
PRICE = -5918 + 32.9 HOUSESIZE + 43646 LOTSIZE + 10394 BATHROOMS.

Predictor     Coef  SE Coef       T      P
Constant     -5918    13612   -0.43  0.679
HOUSESIZE   32.945    9.069    3.63  0.011
LOTSIZE      43646    29384    1.49  0.188
BATHROOMS    10394     6863    1.51  0.181

S = 5269.97   R-Sq = 97.4%   R-Sq(adj) = 96.0%

Analysis of Variance

Source          DF           SS          MS      F      P
Regression       3   6158964520  2052988173  73.92  0.000
Residual Error   6    166635480    27772580
Total            9   6325600000

Predicted Values for New Observations

New Obs     Fit   SE Fit       95% CI            95% PI
1  146075     2998  (138738, 153412)  (131239, 160912)
1  320659   118964  ( 29565, 611752)  ( 29280, 612038)XX

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

Values of Predictors for New Observations

New Obs   HOUSESIZE  LOTSIZE  BATHROOMS
1        2500     1.00       2.50
1        2500     5.00       2.50

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-tests on , , (use two tailed test with (
d. Predict the selling price for an individual home having house size of 2,500 sq. ft, lot size of 1 acre, and 2.5 bathrooms. Use both a point estimate and the appropriate interval estimate. (Points : 31)

 Page:  1  2  3 Time Remaining:

Bottom of Form

Bottom of Form

 Subject Mathematics Due By (Pacific Time) 10/22/2013 12:00 am
TutorRating
pallavi

Chat Now!

out of 1971 reviews
amosmm

Chat Now!

out of 766 reviews
PhyzKyd

Chat Now!

out of 1164 reviews
rajdeep77

Chat Now!

out of 721 reviews
sctys

Chat Now!

out of 1600 reviews

Chat Now!

out of 770 reviews
topnotcher

Chat Now!

out of 766 reviews
XXXIAO

Chat Now!

out of 680 reviews