STAT 30100 Elementary Statistical Methods I
Order ID 53563633773 Type Essay Writer Level Masters Style APA Sources/References 4 Perfect Number of Pages to Order 5-10 Pages Description/Paper Instructions
STAT 30100: Elementary Statistical Methods I
Department of Mathematical Sciences
School of Science, IUPUI
Project # 3
Name:________________________________________________________
Important Instructions:
You must work independently to answer all questions. Provide complete and clear explanations to all questions. Graphs must be labeled for clear communication. (Remember the importance of context throughout!) Your project must be typed, easy to read and have the answer to each question identified by question number. Copy and paste the specified StatCrunch output, including graphs and number summaries, into the specified table. The indicated StatCrunch output MUST appear with the discussion, not as separate pages. Also, consider at least three decimals for your calculation throughout the project.
Problem # 1
The manager of a local soft-drink bottling company believes that when a new beverage-dispensing machine is set to dispense 7 ounces, it in fact dispenses an amount x at random anywhere between 6.5 and 7.5 ounces, inclusive. Suppose x has a uniform probability distribution.
Now we will explore the following questions or ideas.
(a) Using calculator, find the mean and standard deviation of the variable x. [½ + ½ = 1 pt]
(b) Generate 5000 samples of 50 observations each from the uniform distribution.
NO RESULTS TO BE REPORTED
[ StatCrunch: Data -> Simulate data -> Uniform (Rows: 5000, Columns: 50, Uniform parameters a: 6.5, b: 7.5) -> Simulate ]
Note that each row indicates a sample consisting of 50 data values.
(c) Calculate the 5000 sample means. NO RESULTS TO BE REPORTED
[ StatCrunch: Stat-> Summary Stats ->Rows (select all variables from left to right)
Select next
Keep only mean on the right side of the box by clicking each on the left
side except mean
Check mark at “Store output in data table”
Calculate
You will see a new column has been added named “Row Mean” in the dataset. This Row
mean is the mean of each sample.
(d) By the Central Limit Theorem, we know the variable “Row Mean” has an approximate Normal distribution.
- What are the parameter values? [½ + ½ = 1 pt]
[ StatCrunch: Go to Stat -> Summary Stats -> Column (select Row Mean) -> Calculate
Report mean and standard deviation only ]
(ii) Draw a histogram of “Row Mean” with the appropriate Normal PDF overlaid. Does this graph look as you would have expected? [½ + ½ = 1 pt]
[ StatCrunch: GO TO Graphics -> Histogram -> Choose the variable Row Mean -> Next ->
Next-> Choose Overlay density Normal -> Next
X axis label: Means of 5000 samples
Y axis label: Frequency
Title: Histogram of Normal Distribution Exploration by the CLT ]
Click on Create Graph.
(e) Now pretend that μ is unknown, but is still known. Calculate the margin of error(ME) ) for a 95% confidence interval for μ based on a sample of size n = 50. [1 pt]
(f) Imagine calculating a 95% CI for μ using each of the 5000 samples. Of the 5000 CIs, how many would you expect to contain the true value of μ? Explain. [ ½ pt]
(g) Calculate the lower and upper limits of the 95% CIs. NO RESULTS TO BE REPORTED
[ StatCrunch: GO TO Data->Compute expression -> “Row Mean”-ME [ ½ pt]
GIVE New column name: lower
SIMILARLY DO “Row Mean”+ME
GIVE New column name: upper ]
(h) How many of the 5000 CIs covered μ? Is this consistent with your expectations in part (f)?
[½ + ½ = 1 pt]
[ StatCrunch: GO TO Data -> Compute expression
TYPE: between( , lower, upper)
NOTE the value of comes from part (a)
GIVE new column name: tallycount
Again, GO TO Data -> Compute expression
GIVE new column name: tallycount1
GO TO Stat -> Tables-> Frequency (select variable tallycount1) and see the percentage for 1 ]
Problem # 2
Studies were conducted in Los Angeles to determine the carbon monoxide (CO) concentration near freeways. The basic technique used was to capture air samples in special bags and to then determine the carbon monoxide concentration by using a spectrophotometer. The measurements in ppm (parts per million) over a sampled period during the year can be found in the Excel file CARBON.xlsx via Oncourse. Find a 90% confidence interval for µ, the mean CO concentration (in ppm) during the year.
Consider the following steps for your answer.
- Label the parameter.[1 pt]
- Verify all required conditions. (using StatCrunc, produce a boxplot to verify the normality condition) [3 pts]
- Interval calculations. (Both StatCrunch output and manual calculation must be reported; note that answer should be same in both cases) [2+2 = 4 pts]
StatCrunch output:
Manual calculation:
- Interpret your result in part (iii) in the context of the problem.[1 pt]
Problem # 3
In a number of previous Phase I and II studies of male, non-insulin-dependent diabetic (NIDDM) patients conducted by Mylitech Biosystems, Inc., the mean body mass index (BMI) was found to be 28.4. An investigator has 16 male NIDDM patients enrolled in a new study and wants to know if the BMI from this sample is consistent with previous findings. BMI is computed as the ratio of weight in kilograms to the square of the height in meters. The Excel data file BMI.xlsx shows the BMI for 16 males. Conduct a hypothesis test at 5% level of significance to answer the question.
Consider the following steps for your hypotheses test.
- Formulate the hypotheses. (Level the parameter, null hypothesis, alternative hypothesis)[2 pts.]
- Test statistic. (Name of the test you are going to use and verify all required conditions for your test using the data; using StatCrunch, produce a boxplot to verify the normality condition) [3 pts.]
- Calculation of your proposed test statistic and p-value. (Both StatCrunch output and manual calculation must be reported; note that answer should be same in both cases) [3 pts.]
StatCrunch output:
Manual calculation:
- Decision and conclusion in the context. [2 pts.]
RUBRIC
QUALITY OF RESPONSE NO RESPONSE POOR / UNSATISFACTORY SATISFACTORY GOOD EXCELLENT Content (worth a maximum of 50% of the total points) Zero points: Student failed to submit the final paper. 20 points out of 50: The essay illustrates poor understanding of the relevant material by failing to address or incorrectly addressing the relevant content; failing to identify or inaccurately explaining/defining key concepts/ideas; ignoring or incorrectly explaining key points/claims and the reasoning behind them; and/or incorrectly or inappropriately using terminology; and elements of the response are lacking. 30 points out of 50: The essay illustrates a rudimentary understanding of the relevant material by mentioning but not full explaining the relevant content; identifying some of the key concepts/ideas though failing to fully or accurately explain many of them; using terminology, though sometimes inaccurately or inappropriately; and/or incorporating some key claims/points but failing to explain the reasoning behind them or doing so inaccurately. Elements of the required response may also be lacking. 40 points out of 50: The essay illustrates solid understanding of the relevant material by correctly addressing most of the relevant content; identifying and explaining most of the key concepts/ideas; using correct terminology; explaining the reasoning behind most of the key points/claims; and/or where necessary or useful, substantiating some points with accurate examples. The answer is complete. 50 points: The essay illustrates exemplary understanding of the relevant material by thoroughly and correctly addressing the relevant content; identifying and explaining all of the key concepts/ideas; using correct terminology explaining the reasoning behind key points/claims and substantiating, as necessary/useful, points with several accurate and illuminating examples. No aspects of the required answer are missing. Use of Sources (worth a maximum of 20% of the total points). Zero points: Student failed to include citations and/or references. Or the student failed to submit a final paper. 5 out 20 points: Sources are seldom cited to support statements and/or format of citations are not recognizable as APA 6th Edition format. There are major errors in the formation of the references and citations. And/or there is a major reliance on highly questionable. The Student fails to provide an adequate synthesis of research collected for the paper. 10 out 20 points: References to scholarly sources are occasionally given; many statements seem unsubstantiated. Frequent errors in APA 6th Edition format, leaving the reader confused about the source of the information. There are significant errors of the formation in the references and citations. And/or there is a significant use of highly questionable sources. 15 out 20 points: Credible Scholarly sources are used effectively support claims and are, for the most part, clear and fairly represented. APA 6th Edition is used with only a few minor errors. There are minor errors in reference and/or citations. And/or there is some use of questionable sources. 20 points: Credible scholarly sources are used to give compelling evidence to support claims and are clearly and fairly represented. APA 6th Edition format is used accurately and consistently. The student uses above the maximum required references in the development of the assignment. Grammar (worth maximum of 20% of total points) Zero points: Student failed to submit the final paper. 5 points out of 20: The paper does not communicate ideas/points clearly due to inappropriate use of terminology and vague language; thoughts and sentences are disjointed or incomprehensible; organization lacking; and/or numerous grammatical, spelling/punctuation errors 10 points out 20: The paper is often unclear and difficult to follow due to some inappropriate terminology and/or vague language; ideas may be fragmented, wandering and/or repetitive; poor organization; and/or some grammatical, spelling, punctuation errors 15 points out of 20: The paper is mostly clear as a result of appropriate use of terminology and minimal vagueness; no tangents and no repetition; fairly good organization; almost perfect grammar, spelling, punctuation, and word usage. 20 points: The paper is clear, concise, and a pleasure to read as a result of appropriate and precise use of terminology; total coherence of thoughts and presentation and logical organization; and the essay is error free. Structure of the Paper (worth 10% of total points) Zero points: Student failed to submit the final paper. 3 points out of 10: Student needs to develop better formatting skills. The paper omits significant structural elements required for and APA 6th edition paper. Formatting of the paper has major flaws. The paper does not conform to APA 6th edition requirements whatsoever. 5 points out of 10: Appearance of final paper demonstrates the student’s limited ability to format the paper. There are significant errors in formatting and/or the total omission of major components of an APA 6th edition paper. They can include the omission of the cover page, abstract, and page numbers. Additionally the page has major formatting issues with spacing or paragraph formation. Font size might not conform to size requirements. The student also significantly writes too large or too short of and paper 7 points out of 10: Research paper presents an above-average use of formatting skills. The paper has slight errors within the paper. This can include small errors or omissions with the cover page, abstract, page number, and headers. There could be also slight formatting issues with the document spacing or the font Additionally the paper might slightly exceed or undershoot the specific number of required written pages for the assignment. 10 points: Student provides a high-caliber, formatted paper. This includes an APA 6th edition cover page, abstract, page number, headers and is double spaced in 12’ Times Roman Font. Additionally, the paper conforms to the specific number of required written pages and neither goes over or under the specified length of the paper. GET THIS PROJECT NOW BY CLICKING ON THIS LINK TO PLACE THE ORDER
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