# Math 533- 64541 | Mathematics homework help

1. (TCO A) Consider the following sample data on the age of the 30 employees that were laid off recently from DVC Inc.

21         38         20         26         37         52         37         24         45         20

50         49         44         30         29         42         56         46         60         30

32         25         47         55         38         25         20         29         32         30

a. Compute the mean, median, mode, and standard deviation, Q1, Q3, Min, and Max for the above sample data on age of employees being laid off.

b. In the context of this situation, interpret the Median, Q1, and Q3. (Points : 33)

2. (TCO B) Consider the following data on newly hired employees in relation to which part of the country they were born and their highest degree attained.

 HS BS MS PHD Total East 3 5 2 1 11 Midwest 7 9 2 0 18 South 5 8 6 2 21 West 1 7 8 6 22 Total 16 29 18 9 72

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

a. is from the Midwest.
b. is from the South and has a PHD.
c. is from the West, given that person only holds a MS degree. (Points : 18)

3. (TCO B) A source in the Internal Revenue Service has stated that historically 90% of federal tax returns filed are free of arithmetic errors. A random sample of 25 returns are selected and checked carefully for arithmetic errors. Assuming independence, find the probability that

a. all 25 returns are free of arithmetic errors.
b. at most 23 returns are free of arithmetic errors.
c. more than 17 are free of arithmetic errors. (Points : 18)

4. (TCO B) The Bank of Connecticut issues Visa and Mastercard credit cards. The balances on these credit cards follow a normal distribution with a mean of $845 and standard deviation of$270.

a. What percentage of balances is below $1,200? b. What percentage of balances is between$600 and \$1,000?
c. Find the 12th percentile for balance (i.e., find the cutoff for the lowest 12% of balances). (Points : 18)

Question 5.

6. (TCO C) The personnel manager of a large firm wants to find the percentage of employee absences that occur on Fridays. A random selection of 500 employee absences is taken from work records over the past several years. The data reveals that 220 of the 500 employee absences were on Fridays.

a. Compute the 99% confidence interval for the population proportion of absences that are on Friday.
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)

8. (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 (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 conclude that installation is feasible at this location (using a = .10)? (Points : 24)
1. (TCO E) McCave Development Enterprises is considering whether to build a shopping mall in Statesville. The manager wants you to analyze the relationship between mall size and the rate of return on invested capital. You select a random sample of 16 cities similar to Statesville in demographic and economic characteristics and collect the following data on FOOTAGE (in 10,000 square feet) and RETURN (rate of return as a %).

 RETURN FOOTAGE PREDICT 18.3 12.8 15.0 11.7 18.6 7.5 19.5 10.3 17.5 14.3 15.4 14.2 9.8 21.4 11.4 18.6 14.5 16.7 16.3 15.5 19.0 9.8 17.0 14.2 15.1 16.2 19.5 12.8 10.9 19.4 16.3 15.0 16.3 15.4

Regression Analysis: RETURN versus FOOTAGE

The regression equation is
RETURN = 30.0 – 0.943 FOOTAGE

Predictor      Coef  SE Coef       T      P
Constant     29.976    1.238   24.22  0.000
FOOTAGE    -0.94257  0.07921  -11.90  0.000

S = 0.969721   R-Sq = 91.0%   R-Sq(adj) = 90.4%

Analysis of Variance

Source          DF      SS      MS       F      P
Regression       1  133.15  133.15  141.59  0.000
Residual Error  14   13.17    0.94
Total           15  146.31

Predicted Values for New Observations

New Obs     Fit  SE Fit       95% CI            95% PI
1  15.838   0.244  (15.315, 16.360)  (13.693, 17.982)
2  22.907   0.666  (21.479, 24.334)  (20.384, 25.429)X

X denotes a point that is an outlier in the predictors.

Values of Predictors for New Observations

New Obs  FOOTAGE
1     15.0
2      7.5

Correlations: RETURN, FOOTAGE

Pearson correlation of RETURN and FOOTAGE = -0.954
P-Value = 0.000

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 Footage can be used to predict Return? 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 rate of return on capital investment for malls that have square footage of 150,000. Interpret this interval.
g. Find the 95% prediction interval for the rate of return on capital investment for a mall that has square footage of 150,000. Interpret this interval.
h. What can we say about the rate of return on capital investment for a mall that has square footage of 75,000?
(Points : 48)

1. (TCO E) An insurance firm wishes to study the relationship between driving experience (X1, in years), number of driving violations in the past three years (X2), and current monthly auto insurance premium (Y).  A sample of 12 insured drivers is selected at random.  The data is given below (in MINITAB):

 Y X1 X2 Predict X1 Predict X2 74 5 2 8 1 38 14 0 50 6 1 63 10 3 97 4 6 55 8 2 57 11 3 43 16 1 99 3 5 46 9 1 35 19 0 60 13 3

Regression Analysis: Y versus X1, X2

The regression equation is
Y = 55.1 – 1.37 X1 + 8.05 X2

Predictor     Coef  SE Coef      T      P
Constant    55.138    7.309   7.54  0.000
X1         -1.3736   0.4885  -2.81  0.020
X2           8.053    1.307   6.16  0.000

S = 6.07296   R-Sq = 93.1%   R-Sq(adj) = 91.6%

Analysis of Variance

Source          DF      SS      MS      F      P
Regression       2  4490.3  2245.2  60.88  0.000
Residual Error   9   331.9    36.9
Total           11  4822.3

Predicted Values for New Observations

New Obs    Fit  SE Fit      95% CI          95% PI
1  52.20    2.91  (45.62, 58.79)  (36.97, 67.44)

Values of Predictors for New Observations

New Obs    X1    X2
1  8.00  1.00

Correlations: Y, X1, X2

Y      X1
X1  -0.800
0.002

X2   0.933  -0.660
0.000   0.020

Cell Contents: Pearson correlation
P-Value

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  and on  (use two tailed test with (= .05). Interpret your results.
d. Predict the monthly premium for an individual having 8 years of driving experience and 1 driving violation during the past 3 years. Use both a point estimate and the appropriate interval estimate.
(Points : 31)