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Category: Calculus and Above
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# How fast can you turn around 3 statistic questions?

### Customer Question

How fast can you turn around 3 statistic questions?
Submitted: 2 years ago.
Category: Calculus and Above
Expert:  Ryan replied 2 years ago.

Hi,

Welcome! Thank you for using the site.

It really depends on the questions. If they are short and straight-forward, or if I already have solutions on file, then I can return the solutions to you in a matter of a few minutes. More complicated problems will take longer. Please post the problems that you need help with and I'll be happy to take a look at them and let you know how long it might take.

Thanks,

Ryan

Customer: replied 2 years ago.
1. 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.2. 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?1. (TCO E) An official of a major racetrack would like to develop a model to estimate the amount of money wagered (Y, WAGERED, in millions of dollars) based on attendance (X1, ATTENDANCE, in \$1,000s) and whether it rains (X2, RAIN, with 0=no rain, 1=rain). A random sample of 10 days was selected with the results found below.
ATTENDANCE RAIN WAGERED
14.5 1 7
21.2 1 8.3
11.6 1 6.2
31.7 0 11
46.6 0 12.7
31.4 0 10.2
40 0 11.5
21 1 8
16.3 1 7.1
32.1 0 10.4
Correlations: ATTENDANCE, RAIN, WAGERED
ATTENDANCE RAIN
RAIN -0.888
0.001
WAGERED 0.989 -0.918
0.000 0.000
Cell Contents: Pearson correlation
P-Value
Regression Analysis: WAGERED versus ATTENDANCE, RAIN
The regression equation is
WAGERED = 5.45 + 0.157 ATTENDANCE - 0.787 RAIN.
Predictor Coef SE Coef T P
Constant 5.4495 0.6957 7.83 0.000
ATTENDANCE 0.15705 0.01878 8.36 0.000
RAIN -0.7869 0.4109 -1.92 0.097
S = 0.298151 R-Sq = 98.6% R-Sq(adj) = 98.2%
Analysis of Variance
Source DF SS MS F P
Regression 2 43.082 21.541 242.32 0.000
Residual Error 7 0.622 0.089
Total 9 43.704
Predicted Values for New Observations
New Obs Fit SE Fit 95% CI 95% PI
1 10.1611 0.1790 (9.7379, 10.5844) (9.3388, 10.9835)
Values of Predictors for New Observations
New Obs ATTENDANCE RAIN
1 30.0 0.000000
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 amount wagered for a single day where the attendance is 30,000 and it does not rain. Use both a point estimate and the appropriate interval estimate. (Points : 31)
Expert:  Ryan replied 2 years ago.

Thanks. I'm looking these over right now.

Expert:  Ryan replied 2 years ago.

Hi again,

I have a solution for the first problem on file, but I don't seem to have anything for the other two. I'll have to do those from scratch. I wouldn't expect them to take very long though.

For the last two questions, however, there seems to be some information missing in the Word file that you attached. In part b of the second of the three problems there is something missing between "Find and interpret" and "in the context of this problem." What are we supposed to be doing in this part?

Similarly, in part c of the last problem, it states to "perform the multiple regression t-tests on", and there is a large blank space in the document.

Can you help clarify what is being asked for in those two parts?

Thanks,

Ryan

Customer: replied 2 years ago.
Never mind thanks
Expert:  Ryan replied 2 years ago.

Ok, no problem.