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Questions And Asnwers

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Subject
Data Analytics
School
Excelsior College
Type
Homework
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Questions and Answers
First Name and Last Name
The University of ………………….
Course Code: Name of Course
Instructor Name
Due Date

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2
1 Run a two-sample t-test for means to determine if the difference in Home Price for
homes with a fireplace and those without a fireplace is statistically significant.
Using that information, how much does having a fireplace change the value of a home?
How do your results compare to the surveys discussed above? What could explain why
your "fireplace value" is different than the values reported in the surveys?
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Two Sample t-test for Population Means - Sigmas
Unknown- Raw Data
Sample 1 mean x
1 =
239913.955
Sample 2 mean x
2 =
174653.350
Sample 1 Standard Dev. s1 =
102357.585
Sample 2 Standard Dev. s2 =
78836.347
Sample 1 size n1 =
988
Sample 2 size n2 =
740
Mean Difference Md = µ1 -µ2
0
Significance Level α
0.050
2. Select Variance
Variances σ2 are
≠ Not Equal
D.F.
739.000
Test Statistic, Standardized Test Statistic
Test Statistic μ1 - μ2 =
65260.60547
Standard Error
4359.2666
Standardized Test Statistic t =
14.97055
Two-Tail Test
Lower Critical Value
-1.9632
Upper Critical Value
1.9632
p-Value
0.00000
Left-Tail Test
Lower Critical Value
-1.6469
p-Value
1.00000

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3
Right-Tail Test
Upper Critical Value
1.6469
p-Value
0.00000
Based on the two-tail test, the null hypothesis can be rejected as the p-value is lesser than 0.05.
Because of that, the difference in home prices for homes with a fireplace and those without a
fireplace is statistically significant. Considering the mean values, if there is a fireplace the price
will be $239,913.96 and it is $65,260.60 higher than a price of a house that does not have a
fireplace. However, the survey results can be different from the results due to non-uniformity of
the distributions.
2a 2a. Make a scatter plot of Home Price, the response variable (y), and Living Area, the
predictor variable (x).
2b 2b. Add a trend line with equation and R2 to the scatter chart.
3a 3a. Run a simple linear regression between Home Price, the response variable (y), and
Living Area, the predictor variable (x). Use all records in the data set.
y = 113.12x + 13439
R² = 0.5075
$-
$100,000
$200,000
$300,000
$400,000
$500,000
$600,000
$700,000
$800,000
$900,000
0 1000 2000 3000 4000 5000 6000
Home Price
Living Area
Home Price

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Questions and Answers First Name and Last Name The University of …………………. Course Code: Name of Course Instructor Name Due Date 2 1 Run a two-sample t-test for means to determine if the difference in Home Price for homes with a fireplace and those without a fireplace is statistically significant. Using that information, how much does having a fireplace change the value of a home? How do your results compare to the surveys discussed above? What could explain why your "fireplace value" is different than the values reported in the surveys? 𝐻0 : 𝜇𝑤𝑖𝑡ℎ 𝑓𝑖𝑟𝑒𝑝𝑙𝑎𝑐𝑒 − 𝜇𝑤𝑖𝑡ℎ𝑜𝑢𝑡 𝑓𝑖𝑟𝑒𝑝𝑙𝑎𝑐𝑒 = 0 𝐻𝛼 : 𝜇𝑤𝑖𝑡ℎ 𝑓𝑖𝑟𝑒𝑝𝑙𝑎𝑐𝑒 − 𝜇𝑤𝑖𝑡ℎ𝑜𝑢𝑡 𝑓𝑖𝑟𝑒𝑝𝑙𝑎𝑐𝑒 ≠ 0 Two Sample t-test for Population Means - Sigmas Unknown- Raw Data Sample 1 mean x̅1 = Sample 2 mean x̅2 = Sample 1 Standard Dev. s1 = Sample 2 Standard Dev. s2 = Sample 1 size n1 = Sample 2 size n2 = Mean Difference Md = µ1 -µ2 Significance Level α 239913.955 174653.350 102357.585 78836.347 988 740 0 0.050 2. Select Variance Variances σ2 are ≠ Not Equal D.F. 739.000 Test Statistic, Standardized Test Statistic Test Statistic μ1 - μ2 = 65260.60547 Standard Error 4359.2666 Standardized Test Statistic t = 14.97055 Two-Tail Test Lower Critical Value Upper Critical Value p-Value -1.9632 1.9632 0.00000 Left-Tail Test Lower Critical Val ...
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