stat 250 data analysis

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lpxbxb123

Mathematics

Description

It is a data analysis and required to use StatCrunch. requirement and data need to solve are upload.

Elements of good technical writing:

Use complete and coherent sentences to answer the questions.

Again, graphs must be appropriately titled and should refer to the context of the question.

Again, graphical displays must include labels with units if appropriate for each axis.

Units should always be included when referring to numerical values.

When making a comparison you must use comparative language, such as “greater than”, “less than”, or “about the same as.”

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STAT 250 Fall 2017 Data Analysis Assignment 5 Your submitted document should include the following items. Points will be deducted if the following are not included. For an example of formatting, see the sample problem/solution document posted on Blackboard. 1. 2. 3. 4. 5. 6. Type your Name and STAT 250 with your correct section number (e.g. STAT 250-xxx), right justified on the top of page 1 of your document. Type Data Analysis Assignment 5 centered on Page 1 under your name. Number your pages across your entire solutions document. Your document should include the ANSWERS ONLY with each answer labeled by its corresponding number and subpart (there are four problems on this assignment). Keep your solutions in order. You should not include the questions in your submitted document. Generate all requested graphs using StatCrunch. Graphs must be appropriately titled and should refer to the context of the question. Graphical displays must include labels with units if appropriate for each axis. Upload your solutions document onto Blackboard as a Word or pdf document using the link provided by your instructor. Elements of good technical writing: Use complete and coherent sentences to answer the questions. Again, graphs must be appropriately titled and should refer to the context of the question. Again, graphical displays must include labels with units if appropriate for each axis. Units should always be included when referring to numerical values. When making a comparison you must use comparative language, such as “greater than”, “less than”, or “about the same as.” Ensure that all graphs and tables appear on one page and are not split across two pages. Type all mathematical calculations when directed to compute an answer ‘by-hand.’ Pictures of actual handwritten work are not accepted. When writing mathematical expressions into your document you may use either an equation editor or common shortcuts such as: x can be written as sqrt(x), p̂ can be written as p-hat, x can be written as x-bar. 1 Problem 1: Appropriateness of Inference For the following scenarios, answer the questions for each part. In each part, the underlined text is the name of the StatCrunch data set to be used for that part. a) Aluminum Bottles. The aluminum bottle has become popular with beverage manufacturers. Besides being lightweight and requiring less packaging, the aluminum bottle is reported to cool faster and stay cold longer than typical glass bottles. A small brewery tests this claim by obtaining two random samples (one of each type of bottle). Each sample of bottles measured the time in minutes required to chill a bottle of beer from room temperature (75 degrees F) to serving temperature (45 degrees F). i) What is (are) the parameter(s) of interest? Choose one of the following symbols ((the mean of one sample)D (the mean difference from a paired (dependent) design)2 (the mean difference from independent samples) and describe the parameter in context in one sentence. ii) Depending on your answer to part (a), construct one or two histograms and one or two boxplots to visualize the distribution(s) of your sample data. Remember to properly title and label these graphs. Copy and paste these graphs into your document. iii) Describe the shape of the histogram(s) in one sentence. iv) Does the boxplot(s) show any outliers? Answer this question in one sentence. v) Is inference appropriate in this case? Why or why not? Defend your answer using the graphs in two to three sentences. b) Metal Hardness Testing. The manufacturer of hardness testing equipment uses steel-ball indenters to pierce metal that is being tested. However, the manufacturer thinks it would be better to use a diamond indenter so that they can test all types of metal. Because of the differences between the two types of indenters, it is suspected that the two methods will produce different hardness readings. The metal specimens to be tested are large enough so that two indentions can be made. Therefore, the manufacturer wants to use both indenters on each specimen and compare the readings. The order of the indentions will be random. i) What is (are) the parameter(s) of interest? Choose one of the following symbols (the mean of one sample)D (the mean difference from a paired (dependent) design)2 (the mean difference from independent samples) and describe the parameter in contect in one sentence. ii) Depending on your answer to part (a), construct one or two histograms and one or two boxplots to visualize the distribution(s) of your sample data. Remember to properly title and label these graphs. Copy and paste these graphs into your document. 2 iii) Describe the shape of the histogram(s) in one sentence. iv) Does the boxplot(s) show any outliers? Answer this question in one sentence. v) Is inference appropriate in this case? Why or why not? Defend your answer using the graphs in two to three sentences. c) Too Much Salt. A nutritionist claims that children under the age of 10 years are consuming more than the US Food and Drug Administration’s recommended daily allowance of sodium, which is 2400 mg. To test this claim, she obtains a random sample of 18 children under the age of 10 and measures their daily consumption of sodium. i) What is (are) the parameter(s) of interest? Choose one of the following symbols (the mean of one sample)D (the mean difference from a paired (dependent) design)2 (the mean difference from independent samples) and describe the parameter in context in one sentence. ii) Depending on your answer to part (a), construct one or two histograms and one or two boxplots to visualize the distribution(s) of your sample data. Remember to properly title and label these graphs. Copy and paste these graphs into your document. iii) Describe the shape of the histogram(s) in one sentence. iv) Does the boxplot(s) show any outliers? Answer this question in one sentence. v) Is inference appropriate in this case? Why or why not? Defend your answer using the graphs in two to three sentences. Problem 2: Styles of Instruction A researcher wanted to know whether there was a difference in the level of understanding among students learning StatCrunch based on the style of instruction. In a previous semester of STAT 250, Section 1 was taught StatCrunch with video tutorials and Section 2 was taught StatCrunch with written instructions. A random sample of 24 was taken from each section and the students in each sample were given a StatCrunch quiz that tested basic procedures. The data provided in StatCrunch represent the quiz scores the students received. The file is called “Styles of Instruction.” At the 0.01 significance level, can the researcher conclude from these data that there is a significant difference in quiz scores between the two methods of instruction? a) Conduct a full hypothesis test by following the steps below. Enter an answer for each of these steps in your document. i. State the null and alternative hypotheses using correct notation. ii. State the significance level for this problem. 3 iii. Calculate the test statistic “by-hand.” Show the work necessary to obtain the value by typing your work and provide the resulting test statistic. iv. Calculate the p-value using StatCrunch. v. State whether you reject or do not reject the null hypothesis and your reason for your answer in one sentence. vi. State your conclusion in context of the problem (i.e. interpret your results and/or answer the question being posed) in one or two complete sentences. vii. Use StatCrunch (Stat  T Stats …) to verify your test statistic and p-value. Copy and paste this box into your document. b) Construct a 99% confidence interval using the above data. Please do this “by hand” using the formula and showing your work (please type your work, no images accepted here). Then, verify your result using StatCrunch. Copy and paste your StatCrunch result in your document as well. Interpret the confidence interval as we learned in class. Problem 3: Cholesterol The U.S. Department of Health has suggested that a healthy total cholesterol measurement should be 200 mg/dL or less. Records for 28 randomly selected individuals are presented in StatCrunch (the data set is called “Cholesterol”). Test the hypothesis that the mean cholesterol level is more than 200 using a significance level of 0.05. a) Conduct a full hypothesis test by following the steps below. Enter an answer for each of these steps in your document. i. State the null and alternative hypotheses using correct notation. ii. State the significance level for this problem. iii. Calculate the test statistic “by-hand.” Show the work necessary to obtain the value by typing your work and provide the resulting test statistic. iv. Calculate the p-value using StatCrunch. v. State whether you reject or do not reject the null hypothesis and your reason for your answer in one sentence. vi. State your conclusion in context of the problem (i.e. interpret your results and/or answer the question being posed) in one or two complete sentences. vii. Use StatCrunch (Stat  T Stats …) to verify your test statistic and p-value. Copy and paste this box into your document. b) Construct a 95% confidence interval using the above data. Please do this “by hand” using the formula and showing your work (please type your work, no images accepted here). Then, verify your result using StatCrunch. Copy and paste your StatCrunch result in your document as well. Interpret the confidence interval as we learned in class. 4 Problem 4: Red Light Cameras To combat red-light-running crashes, many states are installing red light cameras at dangerous intersections. These cameras photograph the license plates of vehicles that run red lights and automatically issue tickets. How effective are these photo enforcement programs? The Virginia Department of Transportation (VDOT) conducted a comprehensive study of its newly adopted program and published the results in a 2012 study. In one portion of the study, VDOT provided crash data both before and after installation of the cameras at several intersections. The data, measured as the crash rate caused by red light running per intersection per year, for 13 randomly selected intersections in Fairfax County are given in the data file called “Red Light Cameras.” At the 0.10 significance level, test the claim that the installation of the cameras decreased the mean number of crashes at intersections where the cameras were installed. a) No matter what your answer is for part (b(iii)), conduct a full hypothesis test by following the steps below. Enter an answer for each of these steps in your document. i. State the null and alternative hypotheses using correct notation. ii. State the significance level for this problem. iii. Calculate the test statistic “by-hand.” Show the work necessary to obtain the value by typing your work and provide the resulting test statistic. iv. Calculate the p-value using StatCrunch. v. State whether you reject or do not reject the null hypothesis and your reason for your answer in one sentence. vi. State your conclusion in context of the problem (i.e. interpret your results and/or answer the question being posed) in one or two complete sentences. vii. Use StatCrunch (Stat  T Stats …) to verify your test statistic and p-value. Copy and paste this box into your document. b) Construct a 90% confidence interval using the above data. Please do this “by hand” using the formula and showing your work (please type your work, no images accepted here). Then, verify your result using StatCrunch. Copy and paste your StatCrunch result in your document as well. Interpret the confidence interval as we learned in class. 5 Aluminum Glass 71.23 126.11 76.49 124.52 77.59 129.85 103.33 135.58 123.45 137.32 122.33 151.61 76.27 71.09 78.78 149.44 120.09 76.12 99.1 109.97 101.5 141.98 120.48 133.63 140.58 137.37 124.11 143.15 Specimen Steel Ball 1 2 3 4 5 6 7 8 9 10 11 12 Diamond 51 57 61 71 68 53 67 51 54 89 51 70 52 56 61 72 69 55 68 51 56 87 53 73 Salt Intake 2085.9 2286.32 3309.54 3582.43 2970.73 2901.52 2511.39 2525.74 3644.48 2120.5 2330.54 4793.95 3377.41 3150.94 2054.54 2424.74 4320.49 2787.64
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Explanation & Answer

Hello! Please see the following file for discussion - I would like to discuss this with you if you have any concern/question :)

Name
STAT 250-xxx
Data Analysis Assignment 5

a) Aluminum Bottles. The aluminum bottle has become popular with beverage
manufacturers. Besides being lightweight and requiring less packaging, the aluminum
bottle is reported to cool faster and stay cold longer than typical glass bottles. A small
brewery tests this claim by obtaining two random samples (one of each type of bottle).
Each sample of bottles measured the time in minutes required to chill a bottle of beer
from room temperature (75 degrees F) to serving temperature (45 degrees F).
i) What is (are) the parameter(s) of interest? Choose one of the following symbols
((the mean of one sample)D (the mean difference from a paired (dependent)
design)2 (the mean difference from independent samples) and describe the
parameter in context in one sentence.
ANS. The parameter of interest is the mean difference from independent samples,
2.
ii) Depending on your answer to part (a), construct one or two histograms and one or
two boxplots to visualize the distribution(s) of your sample data. Remember to
properly title and label these graphs. Copy and paste these graphs into your
document.

Histogram of Aluminum
4

Frequency

3

2

1

0

70

80

90

1 00

Aluminum

110

1 20

Histogram of Glass
6

Frequency

5

4

3

2

1

0

80

1 00

1 20

1 40

Glass

Boxplot of Aluminum, Glass
1 60
1 50
1 40

Data

1 30
1 20
110
1 00
90
80
70
Aluminum

Glass

iii) Describe the shape of the histogram(s) in one sentence.
The histogram for the resof the Aluminum
iv) Does the boxplot(s) show any outliers? Answer this question in one sentence.
The boxplot for the glass bottles shows two outliers.
v) Is inference appropriate in this case? Why or why not? Defend your answer using the
graphs in two to three sentences.
There is no need for a statistical inference for this case because from the histogram and
from the boxplot, it is apparent that there is a significant difference between the two.
b) Metal Hardness Testing. The manufacturer of hardness testing equipment uses steel-ball
indenters to pierce metal that is being tested. However, the manufacturer thinks it would
be better to use a diamond indenter so that they can test all types of metal. Because of
the differences between the two types of indenters, it is suspected that the two methods
will produce different hardness readings. The metal specimens to be tested are large
enough so that two indentions can be made. Therefore, the manufacturer wants to use
both indenters on each specimen and compare the readings. The order of the indentions
will be random.
i) What is (are) the parameter(s) of interest? Choose one of the following symbols
(the mean of one sample)D (the mean difference from a paired (dependent)
design)2 (the mean difference from independent samples) and describe the
parameter in contest in one sentence.
The parameter of interest is D which is the mean difference between the
indentations of steel ball and diamond measured for each specimen.
ii) Depending on your answer to part (a), construct one or two histograms and one or
two boxplots to visualize the distribution(s) of your sample data. Remember to
properly title and label these graphs. Copy and paste these graphs into your
document.

Histogram of Difference
4

Frequency

3

2

1

0

-3

-2

-1

0

1

2

Difference

Boxplot of Difference
2

Difference

1

0

-1

-2

-3

iii) Describe the shape of the histogram(s) in one sentence.
The shape of the histogram is a little skewed to the left.
iv) Does the boxplot(s) show any outliers? Answer this question in one sentence.
The boxplot does not show any outlier.

v) Is inference appropriate in this case? Why or why not? Defend your answer using the
graphs in two to three sentences.
There is a need to do inference testing for this case since there is no telling from the
plot if the difference between the two is really zero.
c) Too Much Salt. A nutritionist claims that children under the age of 10 years are
consuming more than the US Food and Drug Administration’s recommended daily
allowance of sodium, which is 2400 mg. To test this claim, she obtains a random sample
of 18 children under the age of 10 and measures their daily consumption of sodium.
i) What is (are) the parameter(s) of interest? Choose one of the following symbols
(the mean of one sample)D (the mean difference from a paired (dependent)
design)2 (the mean difference from independent samples) and describe the
parameter in context in one sentence.
The parameter of interest is the mean of one sample, 
ii) Depending on your answer to part (a), construct one or two histograms and one or
two boxplots to visualize the distribution(s) of your sample data. Remember to
properly title and label these graphs. Copy and paste these graphs into your
document.

Histogram of Salt Intake
5

Frequency

4

3

2

1

0

2000

2500

3000

3500

Salt Intake

4000

4500

5000

Boxplot of Salt Intake
5000

4500

Salt Intake

4000

3500

3000

2500

2000

iii) Describe the shape of the histogram(s) in one sentence.
The histogram does not demonstrate a normally distributed data.
iv) Does the boxplot(s) show any outliers? Answer this question in one sentence.
The block does not show any outlier.
v) Is inference appropriate in this case? Why or why not? Defend your answer using
the graphs in two to three sentences.
There is no need ...


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