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Introduction to Managerial StatisticsThis assignment consists
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Introduction to Managerial Statistics
This assignment consists of four datasets
1. Clouds were randomly seeded or not with silver nitrate. Rainfall amounts were recorded from the clouds. The purpose of the experiment was to determine if cloud seeding increases rainfall. The following data is obtained:
Seeded: 2745.6, 1697.8, 1656, 978, 703.4, 489.1, 430, 334.1, 302.8, 274.7, 274.7, 255, 242.5, 200.7, 198.6, 129.6, 119, 118.3, 115.3, 92.4, 40.6, 32.7, 31.4, 17.5, 7.7, 4.1
Unseeded: 1202.6, 830.1, 372.4, 345.5, 321.2, 244.3, 163, 147.8, 95, 87, 81.2, 68.5, 47.3, 41.1, 36.6, 29, 28.6, 26.3, 26.1, 24.4, 21.7, 17.3, 11.5, 4.9, 4.9, 1
a) For each data set, find the mean and standard deviation.
b) While we have a before and after scenario, the treatments were not performed on the same subjects (clouds) so we could use a pooled (not paired) ttest to determine if the cloud seeding was effective. A ttest requires certain assumptions, including normality and constant variance. Construct a boxplot for the unseeded and seeded data. Based on the boxplots, does the data appear symmetric? Do the variances appear to be equal?
c) Transformations are a common method of “fixing” datasets that do not meet required assumptions. Transforming a data set is applying an invertible, one to one transformation to the data, replacing the data point y with z=f(y). One of the most common transformations is the log transform. Apply the log transform to the data, replacing each data point y with z=ln(y).
d) Construct a boxplot for the transformed data. Does the transformed data appear to be symmetric? Do the variances appear to be equal with the transformed data?
e) Perform a pooled ttest on the transformed data to determine the effectiveness of cloud seeding. Choose the level of significance, and find the critical value for this level of significance. State the forma null and the alternative hypothesis. What is the pvalue? Based on the ttest, what is your conclusion about the effect of cloud seeding on rainfall?
2. This dataset contains the labor force participation rate (LFPR) of women in 19 cities in the United States in each of two years (1968 and 1972). The data help to measure the growing presence of women in the labor force over this period.
City 1972 1968
N.Y. .45 .42
L.A. .50 .50
Chicago .52 .52
Philadelphia .45 .45
Detroit .46 .43
San Francisco .55 .55
Boston .60 .45
Pitt. .49 .34
St. Louis .35 .45
Connecticut .55 .54
Wash., D.C. .52 .42
Cinn. .53 .51
Baltimore .57 .49
Newark .53 .54
Minn/St. Paul .59 .50
Buffalo .64 .58
Houston .50 .49
Patterson .57 .56
Dallas .64 .63
It may seem reasonable to compare LFPR rates in the two years with a pooled ttest since the United States did not change much from 1968 to 1972. However, the data are also naturally paired because the measurements were made in the same cities for each of the two years. We can compare each city in 1972 to its own value in 1968.
a) Construct a histogram for both years. Be sure to use the same number of groups or bins for each year. Compare the two histograms. Do they appear the same or different? If you can plot each histogram on the same graph, it might make it easier to see similarities or differences.
b) What is the sampling distribution for the mean? Would you use a normal or a tdistribution? Why? Find the 95% confidence intervals for the mean for each year (1968 and 1972). Based on the two confidence intervals, would you conclude the LFPR in 1968 and 1972 are the same or different?
c) In order to perform a paired ttest, we need to make sure the data is approximately normal and the variances are the same. Construct and interpret boxplots for both years.
d) Now perform a pooled ttest to test the hypothesis that the mean LFPR for 1968 and the mean LFPR for 1972 are the same, using significance level =0.05. State the null and the alternative hypothesis, and find the critical value. Find the pvalue. What is your conclusion?
e) Now perform a paired ttest on the data, using the same null and alternative hypothesis, and the same significance level as part d. State the null and the alternative hypothesis, and find the critical value. Find the pvalue. What is your conclusion? How does this compare to the results from the pooled test? Explain the reasons for the differences, if any.
3. Results of a study of gas chromatography, a technique which is used to detect very small amounts of a substance. Five measurements were taken for each of four specimens containing different amounts of the substance. The amount of the substance in each specimen was determined before the experiment. The response variable is the output reading from the gas chromatograph. The purpose of the study is to calibrate the chromatograph by relating the actual amount of the substance to the chromatograph reading.
Variable Names:
1. amount: amount of substance in the specimen (nanograms)
2. response: output reading from the gas chromatograph
amount response
0.25 6.55
0.25 7.98
0.25 6.54
0.25 6.37
0.25 7.96
1.00 29.7
1.00 30.0
1.00 30.1
1.00 29.5
1.00 29.1
5.00 211
5.00 204
5.00 212
5.00 213
5.00 205
20.00 929
20.00 905
20.00 922
20.00 928
20.00 919
a) Perform a linear regression with amount as the independent variable and response as the dependent variable. What is the fitted equation? What are 95% confidence intervals for the regression coefficients?
b) Perform a goodness of fit test, stating the null and alternative hypotheses. Interpret the results of the test.
c) Plot the residuals and assess whether the variance is constant. Create a qqnormal plot and determine whether the errors appear normally distributed.
d) Based on the goodness of fit test and the residual diagnostics, do you have a good model? Why or why not?
4. The data below consists of heights of singers in the NY Choral Society in 1979, selfreported, to the nearest inch. Voice parts in order from highest pitch to lowest pitch are Soprano, Alto, Tenor, Bass. The first two are female voices and the last two are male voices. One can examine how height varies across voice range, or make comparisons of sopranos and altos and separate comparisons of tenors and basses. There is some evidence of the shortest singers reporting greater heights, possibly to avoid standing in the front row in a concert. a) Perform an ANOVA, with height as the response and voice range as the factor, and interpret the results. b) Perform a hypothesis test to determine if female singers are shorter on average than male singers.
Variable Names:
1. Soprano: Heights of sopranos (in inches)
2. Alto: ***** ***** altos (in inches)
3. Tenor: Heights of tenors (in inches)
4. Bass: Heights of basses (in inches)
The Data:
Soprano Alto Tenor Bass
64 65 69 72
62 62 72 70
66 68 71 72
65 67 66 69
60 67 76 73
61 63 74 71
65 67 71 72
66 66 66 68
65 63 68 68
63 72 67 71
67 62 70 66
65 61 65 68
62 66 72 71
65 64 70 73
68 60 68 73
65 61 73 70
63 66 66 68
65 66 68 70
62 66 67 75
65 62 64 68
66 70 71
62 65 70
65 64 74
63 63 70
65 65 75
66 69 75
65 61 69
62 66 72
65 65 71
66 61 70
65 63 71
61 64 68
65 67 70
66 66 75
65 68 72
62 66
Submitted:
1 year ago.
Category:
Calculus and Above
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Expert:
Mr. Gregory White
replied 1 year ago.
Hello, my name is ***** ***** I am one of the homework professionals.
The information you have posted does not show the proper formatting needed for the question and it would be beneficial for me to view the original assignment file if that is possible.
You can upload using a file sharing site such as mediafire.com or wikisend.com and share the link here.
Also, be sure to let me know the deadline to get the resource returned to you.
Here are the steps to use wikisend as it is the easiest and does not require an account. We are not able to get things by email (unfortunately)
1. Go to www.wikisend.com
2. Click on the "Browse" Button
3. Find the file on your computer and select it  this will place the link in the box on the site.
4. Click on "Upload File"
5. This will then open a new window.
6. You will see a box that says "Download Link"  Copy and Paste that weblink in the box here for me.
I can then open your file onto my computer.
You can repeat this for each of the files. Place all the link into one reply box here and then I can open any of the documents.
This will ensure I get the materials quickly.
Thanks and I look forward to trying to assist on this question.
Ask Your Own Calculus and Above Question
Customer:
replied 1 year ago.
Sample solutions:http://wikisend.com/download/463882/Ttest On Sample Example.doc
http://wikisend.com/download/637484/Transformation Example.xls
http://wikisend.com/download/498342/Copy of CEO Salary Data.xls
http://wikisend.com/download/345610/Chapter 4 solutions.pdf
Expert:
Mr. Gregory White
replied 1 year ago.
After going through my resources, I do not have what is necessary to complete at this time.
I am opting out and opening up to the other professionals and messaging a couple who might be able to help.
Someone should be with you shortly.
Ask Your Own Calculus and Above Question
Customer:
replied 1 year ago.
thank you!
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