MTH Hypothesis Testing and Confidence Intervals

  

Using the sample data, perform the hypothesis test for each of the below situations in order to see if there is evidence to support the manager’s belief in each case a.-d.  In each case use the Seven Elements of a Test of Hypothesis, using the a provided explain the conclusion in simple terms.  Also be sure to compute the p-value and interpret.Follow this up with computing confidence intervals for each of the variables described in a.-d., and again interpreting these intervals.Write a report to your manager about the results, distilling down the results in a way that would be understandable to someone who does not know statistics.  Clear explanations and interpretations are critical.I’VE INCLUDED PART A THAT HAS ALREADY BEEN DONE AS WELL AS THE DATA WHICH IS ALSO ATTACHED FOR REFERENCE.Data A.docxData_AJ_DAVIS.xla Format for report:Summary Report (about 1 paragraph on each of the speculations a.-d.)Appendix with all of the steps in hypothesis testing (the format of the Seven Elements of a Test of Hypothesis, in Section 6.2 of your text book) for each speculation a.-d. as well as the confidence intervals, the p-values, and including all Minitab outputQUESTIONS TO ANSWER:a. The average (mean) annual income was greater than $45,000.
H0:µ= 45000
Ha:µ>
a = .   z >  
Descriptive Statistics: Income ($1000)
One-Sample Z
b. The true population proportion of customers who live in a suburban
area is less than 45%.
H0:
Ha:
a =    z < Descriptive Statistics: c. The average (mean) number of years lived in the current home is greater than 8 years. H0:µ Ha:µ a = .  z >
Descriptive Statistics:
d. The average (mean) credit balance for rural customers is less than
$3,200.
H0:µ=
Ha:µ
a =   z < Descriptive Statistics: data_a.docx data_a.docx data_aj_davis.xla Unformatted Attachment Preview PART A: Exploratory Data Analysis Introduction Variable N N* Income ($1000) Size Years Credit Balance($) Variable Income ($1000) Size Years Credit Balance ($) SE Mean Mean StDev Minimum Q1 Median 50 46.02 1.96 13.88 25 33 44.5 50 4.5 0.357 2.525 1 2 4.5 50 9.6 0.641 4.531 1 6 10 50 4153 132 932 2047 3292 4273 Q3 Maximum Skewness Kurtosis 57.25 74 0.26 -1.09 7 8 0 -1.49 13 19 0.06 -0.54 4931 5861 -0.15 -0.72 The above results provides an enlightening insights of the variable. I noticed that the variable salary in the mean and middle are not equivalent, likewise size mean and middle are measure up to and other two variable mean and middle are not equivalent hence they are not symmetric dissemination of the information with the exception of the variable size and variable are absolutely skewed aside from credit Balance. Additionally I see that all kurtosis are negative and under 3 in this manner their information dissemination are platykurtic. Discuss your 1st individual variable, using graphical, numerical summary and interpretation: PART A: Exploratory Data Analysis Histogram of Income ($1,000) 9 8 7 Frequency 6 5 4 3 2 1 0 30 40 50 Income ($1,000) 60 70 Above is a histogram which demonstrates the dispersion of information inside the Income. It is seen in this Histogram that chart of Income demonstrates that the diagram is not symmetrical. This histogram chart has a more extensive ringer shape structure. This chart is more like two diagrams in light of the fact that there is an unmistakable contrast between pay creating from 2040 and from 50-above. There are two isolated bunch; in this manner, the skewedness of this chart is skewed right. Pay has a lower estimation of kurtosis which demonstrates a lower, less particular top. The accompanying table demonstrates the numerical outline of Income: PART A: Exploratory Data Analysis I estimated the P-value of the Income utilizing the Anderson-Darling Normality Test is 0.027
and the A-Squared is 0.85. With the 95% Confidence Interval for Mean, Median, and St Dev are
as taken after:
Discuss your 2nd individual variable, using graphical, numerical summary and
interpretation:
Histogram of Credit Balance($)
14
12
Frequency
10
8
6
4
2
0
2000
2500
3000
3500
4000
Credit Balance($)
4500
5000
5500
For the 2nd individual a histogram is given above which demonstrates the appropriation of
information inside of the Credit Balance. It is seen in this Histogram chart of Credit Balance that
it demonstrates that the diagram is symmetrical except for one exception which is credit offset of
$2,000. This is a typical dissemination with all around acted tails and a solitary top at the center
of the appropriation. Symmetric, is that dissemination can be collapsed around a hub and the two
PART A: Exploratory Data Analysis
sides practically correspond. The accompanying table demonstrates the numerical synopsis of
Credit Balance:
The P-estimation of the Credit Balance utilizing the Anderson-Darling Normality Test is 0.400
and the A-Squared is 0.38. With the 95% Confidence Interval for Mean, Median, and Standard
Deviation are as taken after:
This chart demonstrate that the quantity of the clients current charge card adjust on the store’s
Visa skews more to one side on the grounds that the skewedness is -0.150 and the kurtosis is 0.721 this shows that it have lower worth which demonstrates a lower, less unmistakable crest.
Discuss your 3rd individual variable, using graphical, numerical summary and
interpretation:
PART A: Exploratory Data Analysis
Histogram of Size
16
14
Frequency
12
10
8
6
4
2
0
1
2
3
4
Size
5
6
7
The 3rd individual histogram is given above and it demonstrates the dispersion of information
inside of the Size variable. It is seen in this Histogram chart of Size that it demonstrates that the
diagram is not symmetrical. This histogram diagram has a more extensive ringer shape structure.
The skewedness of this diagram is skewed right. Size has an estimation of kurtosis which
demonstrates a, less unmistakable crest. The accompanying table demonstrates the numerical
rundown of Income:
PART A: Exploratory Data Analysis
The P-estimation of the Size utilizing the Anderson-Darling Normality Test is .005 and the ASquared is 1.59. You can also notice that with the 95% Confidence Interval for Mean, Median,
and St Dev are as taken after:
This diagram demonstrates that the span of two individuals for each family unit is much higher
than others.
Discuss your 1st pairing of variables, using graphical, numerical summary and
interpretation:
Boxplot of Income ($1000)
70
Income ($1000)
60
50
40
30
20
Rural
Suburban
Location
Urban
PART A: Exploratory Data Analysis
Its pairing variable is all about income and Location blending which simply demonstrates that
the Suburban created higher wage. It is seen that the minimum area to produced salary is Rural.
Urban area is fairly in the middle of Suburban and Rural. The N esteem for each of the three area
is 50. The Rural area demonstrates that it is moved altogether to the lower end, it is decidedly
skewed. Additionally, this gives an appraisal of the kurtosis of appropriation. It is a more
extensive box with respect to the stubbles which showed a more extensive top. For both the
Suburban and Urban the crate is moved essentially to the top of the line, it is contrarily skewed.
Both, Suburban and Urban have meager box in respect to the stubbles showed that a high
number of cases are contained inside of the salary. This implied dispersion with a more slender
top. For every one of the three areas, there are no exceptions.
Discuss your 2nd pairing of variables, using graphical, numerical summary and
interpretation
The 2nd pairing variable graph is given above Which is scatter plot of wage versus credit adjust
all the dabs are all in an upward pattern which demonstrated that between those two connections,
they have a positive, cozy relationship. This implies the more pay a family has, the more credit
adjust the family unit will have. The higher the wage, the more credit
PART A: Exploratory Data Analysis
Scatterplot of Income ($1,000) vs Credit Balance($)
80
Income ($1,000)
70
60
50
40
30
20
2000
3000
4000
Credit Balance($)
5000
6000
equalization is bunch together, the lower pay; the credit parity is by all accounts more spread out.
Discuss your 3rd pairing of variables, using graphical, numerical summary and
interpretation:
PART A: Exploratory Data Analysis
Scatterplot of Credit Balance($) vs Years
6000
Credit Balance($)
5000
4000
3000
2000
0
5
10
Years
15
20
In the 3rd pairing variable plot I see that the dots are everywhere and making no specific shape
even with the regression line. This is in between credit parity versus a long time which does not
have any relationship and the two variables are not associated to each other. It demonstrates there
are two or three anomalies from 0-5 years; then from 5-20 years there are a broad of credit offset.
The most Credit Balance is bunch together with the more extended the client live at the present
area. The more they inhabit the present area the more credit offset they will have.
Conclusion:
PART A: Exploratory Data Analysis
I concluded that the years, salary, and credit equalization is all accounts regarding one another in
a proper structure. It is noticed that correlate can’t help suspecting that the more drawn out the
client lives at the present area the more wage and credit parity goes up. Clients living in
Suburban and Urban regions appear to make more salary which could prompt more acknowledge
parity for store. AJ DAVIS retail chains have loads of credit clients that mean from their clients
are individuals living in Suburban and Urban and produced high pay.
PART A: Exploratory Data Analysis
Introduction
Variable
N N*
Income ($1000)
Size
Years
Credit
Balance($)
Variable
Income ($1000)
Size
Years
Credit Balance
($)
SE
Mean
Mean
StDev
Minimum
Q1
Median
50
46.02
1.96
13.88
25
33
44.5
50
4.5
0.357
2.525
1
2
4.5
50
9.6
0.641
4.531
1
6
10
50
4153
132
932
2047
3292
4273
Q3
Maximum
Skewness
Kurtosis
57.25
74
0.26
-1.09
7
8
0
-1.49
13
19
0.06
-0.54
4931
5861
-0.15
-0.72
The above results provides an enlightening insights of the variable. I noticed that the variable
salary in the mean and middle are not equivalent, likewise size mean and middle are measure up
to and other two variable mean and middle are not equivalent hence they are not symmetric
dissemination of the information with the exception of the variable size and variable are
absolutely skewed aside from credit Balance. Additionally I see that all kurtosis are negative and
under 3 in this manner their information dissemination are platykurtic.
Discuss your 1st individual variable, using graphical, numerical summary and
interpretation:
PART A: Exploratory Data Analysis
Histogram of Income ($1,000)
9
8
7
Frequency
6
5
4
3
2
1
0
30
40
50
Income ($1,000)
60
70
Above is a histogram which demonstrates the dispersion of information inside the Income. It is
seen in this Histogram that chart of Income demonstrates that the diagram is not symmetrical.
This histogram chart has a more extensive ringer shape structure. This chart is more like two
diagrams in light of the fact that there is an unmistakable contrast between pay creating from 2040 and from 50-above. There are two isolated bunch; in this manner, the skewedness of this chart
is skewed right. Pay has a lower estimation of kurtosis which demonstrates a lower, less
particular top. The accompanying table demonstrates the numerical outline of Income:
PART A: Exploratory Data Analysis
I estimated the P-value of the Income utilizing the Anderson-Darling Normality Test is 0.027
and the A-Squared is 0.85. With the 95% Confidence Interval for Mean, Median, and St Dev are
as taken after:
Discuss your 2nd individual variable, using graphical, numerical summary and
interpretation:
Histogram of Credit Balance($)
14
12
Frequency
10
8
6
4
2
0
2000
2500
3000
3500
4000
Credit Balance($)
4500
5000
5500
For the 2nd individual a histogram is given above which demonstrates the appropriation of
information inside of the Credit Balance. It is seen in this Histogram chart of Credit Balance that
it demonstrates that the diagram is symmetrical except for one exception which is credit offset of
$2,000. This is a typical dissemination with all around acted tails and a solitary top at the center
of the appropriation. Symmetric, is that dissemination can be collapsed around a hub and the two
PART A: Exploratory Data Analysis
sides practically correspond. The accompanying table demonstrates the numerical synopsis of
Credit Balance:
The P-estimation of the Credit Balance utilizing the Anderson-Darling Normality Test is 0.400
and the A-Squared is 0.38. With the 95% Confidence Interval for Mean, Median, and Standard
Deviation are as taken after:
This chart demonstrate that the quantity of the clients current charge card adjust on the store’s
Visa skews more to one side on the grounds that the skewedness is -0.150 and the kurtosis is 0.721 this shows that it have lower worth which demonstrates a lower, less unmistakable crest.
Discuss your 3rd individual variable, using graphical, numerical summary and
interpretation:
PART A: Exploratory Data Analysis
Histogram of Size
16
14
Frequency
12
10
8
6
4
2
0
1
2
3
4
Size
5
6
7
The 3rd individual histogram is given above and it demonstrates the dispersion of information
inside of the Size variable. It is seen in this Histogram chart of Size that it demonstrates that the
diagram is not symmetrical. This histogram diagram has a more extensive ringer shape structure.
The skewedness of this diagram is skewed right. Size has an estimation of kurtosis which
demonstrates a, less unmistakable crest. The accompanying table demonstrates the numerical
rundown of Income:
PART A: Exploratory Data Analysis
The P-estimation of the Size utilizing the Anderson-Darling Normality Test is .005 and the ASquared is 1.59. You can also notice that with the 95% Confidence Interval for Mean, Median,
and St Dev are as taken after:
This diagram demonstrates that the span of two individuals for each family unit is much higher
than others.
Discuss your 1st pairing of variables, using graphical, numerical summary and
interpretation:
Boxplot of Income ($1000)
70
Income ($1000)
60
50
40
30
20
Rural
Suburban
Location
Urban
PART A: Exploratory Data Analysis
Its pairing variable is all about income and Location blending which simply demonstrates that
the Suburban created higher wage. It is seen that the minimum area to produced salary is Rural.
Urban area is fairly in the middle of Suburban and Rural. The N esteem for each of the three area
is 50. The Rural area demonstrates that it is moved altogether to the lower end, it is decidedly
skewed. Additionally, this gives an appraisal of the kurtosis of appropriation. It is a more
extensive box with respect to the stubbles which showed a more extensive top. For both the
Suburban and Urban the crate is moved essentially to the top of the line, it is contrarily skewed.
Both, Suburban and Urban have meager box in respect to the stubbles showed that a high
number of cases are contained inside of the salary. This implied dispersion with a more slender
top. For every one of the three areas, there are no exceptions.
Discuss your 2nd pairing of variables, using graphical, numerical summary and
interpretation
The 2nd pairing variable graph is given above Which is scatter plot of wage versus credit adjust
all the dabs are all in an upward pattern which demonstrated that between those two connections,
they have a positive, cozy relationship. This implies the more pay a family has, the more credit
adjust the family unit will have. The higher the wage, the more credit
PART A: Exploratory Data Analysis
Scatterplot of Income ($1,000) vs Credit Balance($)
80
Income ($1,000)
70
60
50
40
30
20
2000
3000
4000
Credit Balance($)
5000
6000
equalization is bunch together, the lower pay; the credit parity is by all accounts more spread out.
Discuss your 3rd pairing of variables, using graphical, numerical summary and
interpretation:
PART A: Exploratory Data Analysis
Scatterplot of Credit Balance($) vs Years
6000
Credit Balance($)
5000
4000
3000
2000
0
5
10
Years
15
20
In the 3rd pairing variable plot I see that the dots are everywhere and making no specific shape
even with the regression line. This is in between credit parity versus a long time which does not
have any relationship and the two variables are not associated to each other. It demonstrates there
are two or three anomalies from 0-5 years; then from 5-20 years there are a broad of credit offset.
The most Credit Balance is bunch together with the more extended the client live at the present
area. The more they inhabit the present area the more credit offset they will have.
Conclusion:
PART A: Exploratory Data Analysis
I concluded that the years, salary, and credit equalization is all accounts regarding one another in
a proper structure. It is noticed that correlate can’t help suspecting that the more drawn out the
client lives at the present area the more wage and credit parity goes up. Clients living in
Suburban and Urban regions appear to make more salary which could prompt more acknowledge
parity for store. AJ DAVIS retail chains have loads of credit clients that mean from their clients
are individuals living in Suburban and Urban and produced high pay.

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