(TCO A) Consider the following raw data, which is the result | Complete Solution

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Question 1. 1. (TCO A) Consider the following raw data, which is the result of selecting a random sample of 20 condominium sales in a particular development.  The sale prices are given in thousands of dollars ($1,000s).
            
                        131                   142                   120                   135                   126
                        153                   135                   131                   126                   133
                        147                   137                   130                   126                   140
                        138                   144                   132                   132                   138
 
1a. Compute the mean, median, mode, and standard deviation, Q1, Q3, Min, and Max for the above sample data on sale prices.
1b. In the context of this situation, interpret the Median, Q1, and Q3.
  (Points : 33)
      
       

Question 2. 2. (TCO B) Data has been collected on 200 employees in terms of whether they received training or not and whether they have become productive salespeople or not. Consider the following data.
     Training    No Training    Total
Productive    98    22    120
Not Productive    62    18    80
Total    160    40    200
 
If you choose an employee at random, then find the probability that the employee
 
a. received training and became a productive salesperson.
b. became a productive salesperson.
c. became not productive, given that they had no training. (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) The Federal Government is stepping up efforts to reduce average response times of fire departments to fire calls. The distribution of mean response times to fire calls follows a normal distribution with a mean of 12.8 minutes and a standard deviation of 3.7 minutes.  
 
a. Find the probability that a randomly selected response time is less than 15 minutes.
b. Find the probability that a randomly selected response time is between 13 minutes and 15 minutes.
c. The fastest 20% of fire departments will be singled out for a special safety award. How fast must a fire department be in order to qualify for the special safety award? (Points : 18)
      
       

Question 5. 5. (TCO C) The Ford Motor Company wishes to estimate the mean dollar amount of damage done to a Ford Explorer as a result of a 10 mph crash into the rear bumper of a parked car. The sample results are as follows.
 
Sample Size = 36
Sample Mean = $638
Sample Standard Deviation = $115

a. Construct a 95% confidence interval for the average dollar amount of damage.
b. Interpret this interval.
c. How large a sample size will need to be selected if we wish to have a 95% confidence interval for the average dollar amount of damage with a margin for error of $10? (Points : 18)
      
       

Question 6. 6. (TCO C) A marketing research firm wishes to estimate the proportion of adults who are planning to buy a new car in the next 6 months. A simple random sample of 100 adults led to 22 who were planning to buy a new car in the next 6 months.
 
a. Compute the 95% confidence interval for the proportion of adults who are planning to buy a new car in the next 6 months.
b. Interpret this confidence interval.
c. How large a sample size will need to be selected if we wish to have a 95% confidence interval that is accurate to within 1%. (Points : 18)
      
       

Question 7. 7. (TCO D) An auditor for the U.S. Postal Service wants to examine its special Two-Day Priority mail handling to determine the proportion of parcels that actually arrive within the promised 2-day period. A randomly selected sample of 400 such parcels is found to contain 292 that were delivered on time. Does the sample data provide evidence to conclude that the percentage of on-time parcels is less than 75% (with  = .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 this sample data provide evidence (with = .010), that the percentage of on-time parcels is more than 75%? (Points : 24)
      

Question 8. 8. (TCO D) Bill Smith is the Worthington Township manager. When citizens request a traffic light, the staff assesses the traffic flow at the requested intersection. Township policy requires the installation of a traffic light when an intersection averages more than 150 vehicles per hour. A random sample of 48 vehicle counts is done. The results are as follows:
 
Sample Size = 48
Sample Mean = 158.3 vehicles/hr.
Sample Standard Deviation = 27.6 vehicles/hr.
 
Does the sample data provide evidence to conclude that the installation of the traffic light is warranted (using  = .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. Find the observed p-value for the hypothesis test and interpret this value. What does this mean?
h. Does this sample data provide evidence (with  = 0.10), that the installation of the traffic light is warranted? (Points : 24)
      

1. (TCO E) The Central Company manufactures a certain item once a week in a batch production run. The number of items produced in each run varies from week to week as demand fluctuates. The company is interested in the relationship between the size of the production run (SIZE, X) and the number of person-hours of labor (LABOR, Y). A random sample of 13 production runs is selected, yielding the data below.
 
SIZE    LABOR    PREDICT
40    83    60
30    60    100
70    138    
90    180    
50    97    
60    118    
70    140    
40    75    
80    159    
70    140    
40    75    
80    159    
70    144    
50    90    
60    125    
50    87    

 
 
 
Correlations: SIZE, LABOR
 
Pearson correlation of SIZE and LABOR = 0.990
P-Value = 0.000

 
Regression Analysis: EMP. versus FLIGHTS
 
The regression equation is
LABOR = - 6.16 + 2.07 SIZE
 
 
Predictor     Coef  SE Coef       T      P
Constant    -6.155    5.297   -1.16  0.270
SIZE       2.07371  0.08717   23.79  0.000
 
 
S = 5.20753   R-Sq = 98.1%   R-Sq(adj) = 97.9%
 
 
Analysis of Variance
 
Source          DF      SS      MS       F      P
Regression       1   15349   15349  565.99  0.000
Residual Error  11     298      27
Total           12   15647
 
 
Predicted Values for New Observations
 
New Obs      Fit  SE Fit       95% CI            95% PI
      1   118.27    1.45  (115.07, 121.46)  (106.37, 130.17)
      2   201.22    3.90  (192.64, 209.80)  (186.90, 215.53)X
 
X denotes a point that is an extreme outlier in the predictors.
 
 
Values of Predictors for New Observations
 
New Obs  SIZE
      1    60
      2   100
 
a. Analyze the above output to determine the regression equation.
b. Find and interpret in 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 the size of the production run can be used to predict the total labor hours? 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 the mean total labor hours for all occurrences of having production runs of size 60. Interpret this interval.
g. Find the 95% prediction interval for the total labor hours for one occurrence of a production run of size 60. Interpret this interval.
h. What can we say about the total labor hours when we had a production run of size 100? (Points : 48)

1. (TCO E) The management of an international hotel chain is in the process of evaluating possible sites for a new hotel on a beach resort. As part of the analysis, management is interested in evaluating the relationship between the distance between a hotel and the beach, (Distance, X1 in miles), the number of golf courses on the premises (Golf, X2), and the average occupancy rate (Rate, Y as a %). A sample of 14 existing resort hotels is selected yielding the following results.
 
Distance    Golf    Rate
0.1    2    92
0.1    2    95
0.2    3    96
0.3    3    90
0.4    3    89
0.4    2    86
0.5    2    90
0.6    1    83
0.7    1    85
0.7    1    80
0.8    0    78
0.8    0    76
0.9    0    72
0.9    0    75
 
 
Correlations: Distance, Golf, Rate
 
       Distance     Golf
Golf     -0.859
          0.000
 
Rate     -0.944    0.895
          0.037    0.982
 
 
Cell Contents: Pearson correlation
               P-Value
 
 
Regression Analysis: Rate versus Distance, Golf
 
The regression equation is
Rate = 91.3 - 18.0 Distance + 2.13 Golf.
 
 
Predictor     Coef  SE Coef      T      P
Constant    91.262    3.924  23.26  0.000
Distance   -18.013    4.561  -3.95  0.002
Golf         2.132    1.119   1.91  0.083
 
 
S = 2.39278   R-Sq = 91.8%   R-Sq(adj) = 90.3%
 
 
Analysis of Variance
 
Source          DF      SS      MS      F      P
Regression       2  701.38  350.69  61.25  0.000
Residual Error  11   62.98   5.73
Total           13  764.36
 
 
Predicted Values for New Observations
 
New Obs     Fit  SE Fit       95% CI            95% PI
      1  86.518   0.832  (84.688, 88.349)  (80.943, 92.094)
 
 
Values of Predictors for New Observations
 
New Obs   Distance  Golf
      1      0.500  2.00
 
 
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 , (use two tailed test with (= .10). Interpret your results.
d. Predict the average occupancy rate for a single hotel that is .5 miles from the beach and has two golf courses on the premises. Use both a point estimate and the appropriate interval estimate. (Points : 31)