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In this module you will begin working on Phase 2 of your course project. Continue using the same
data set and variables and perform the following analysis:
Discuss the importance of constructing confidence intervals for the population mean.
What are confidence intervals?
What is a point estimate?
What is the best point estimate for the population mean? Explain.
Why do we need confidence intervals?
Based on your selected topic, evaluate the following:
Find the best point estimate of the population mean.
Construct a 95% confidence interval for the population mean. Assume that your data is normally
distributed and σ, the population standard deviation, is unknown.
Please show your work for the construction of this confidence interval and be sure to use the Equation
Write a statement that correctly interprets the confidence interval in context of your selected topic.
Based on your selected topic, evaluate the following:
Find the best point estimate of the population mean.
Construct a 99% confidence interval for the population mean. Assume that your data is normally
distributed and σ, the population standard deviation, is unknown.
Please show your work for the construction of this confidence interval and be sure to use the Equation
Write a statement that correctly interprets the confidence interval in context of your selected topic.
Compare and contrast your findings for the 95% and 99% confidence interval.
Did you notice any changes in your interval estimate? Explain.
What conclusion(s) can be drawn about your interval estimates when the confidence level is increased?
Explain.
This assignment should be formatted using APA guidelines and a minimum of 2 pages in length.
1/3/2020
STA3215 Section 01 Inferential Statistics and Analytics – …
Name
Statistics Rubric
Description
Rubric Detail
Levels of Achievement
Criteria
Insu cient
Emerging
Competency
Pro ciency
Mastery
Correctness
0.00 %
50.00 %
75.00 %
85.00 %
100.00 %
Less than
half of parts
of all
problems are
solved
correctly.
At least half
of the parts
of all
problems are
solved
correctly.
The majority
of parts of all
problems are
solved
correctly.
Almost all
parts of all
problems are
solved
correctly.
All parts of
all problems
are solved
correctly.
0.00 %
50.00 %
75.00 %
85.00 %
100.00 %
Less than
half of the
calculations
are clearly
shown in
Excel and
have the
proper
formulas
applied.
At least half
of the
calculations
are clearly
shown in
Excel and
have the
proper
formulas
applied.
The majority
of the
calculations
are clearly
shown in
Excel and
have the
proper
formulas
applied.
Almost all
calculations
are clearly
shown in
Excel and
have the
proper
formulas
applied.
All
calculations
are clearly
shown in
Excel and
have the
proper
formulas
applied.
0.00 %
50.00 %
75.00 %
85.00 %
100.00 %
Less than
half of the
explanations,
including
describing all
formulas, are
complete
and correct.
At least half
of the
explanations,
including
describing all
formulas, are
complete
and correct.
The majority
of the
explanations,
including
describing all
formulas are
complete
and correct.
Almost all
explanations,
including
describing all
formulas, are
complete
and correct.
All
explanations,
including
describing all
formulas, are
complete
and correct.
Weight
25.00%
Work Shown
Weight
25.00%
Explanations
Weight
25.00%
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1/2
1/3/2020
STA3215 Section 01 Inferential Statistics and Analytics – …
Levels of Achievement
Criteria
Insu cient
Emerging
Competency
Pro ciency
Mastery
Formatting
0.00 %
50.00 %
75.00 %
85.00 %
100.00 %
Less than
half of the
equations,
expressions,
and variables
are properly
formatted
using the
equation
editor tool in
Microsoft
Word.
At least half
of the
equations,
expressions,
and variables
are properly
formatted
using the
equation
editor tool in
Microsoft
Word.
The majority
of equations,
expressions,
and variables
are properly
formatted
using the
equation
editor tool in
Microsoft
Word.
Almost all
equations,
expressions,
and variables
are properly
formatted
using the
equation
editor tool in
Microsoft
Word.
All
equations,
expressions,
and variables
are properly
formatted
using the
equation
editor tool in
Microsoft
Word.
Weight
25.00%
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Confidence Intervals Overview

Confidence Intervals
o A confidence interval is a range of values used to estimate a population
parameter. They are made by using a point estimate obtained from a sample and
then calculating a margin of error about that point estimate.
o The point estimate is a single value used to estimate a population parameter.
Each parameter type has its own best point estimate statistic.
o Margins of error are computed differently depending on the population parameter
being estimated.
o A confidence level (1 − ) is the probability that the results of our construction of
the confidence interval will contain the population parameter. This Wikipedia
article has a good summary of interpretations with some common
misinterpretations.

Constructing Confidence Intervals for a Population Proportion .
o Best point estimate:
̂ =

o Critical Value: ⁄2
▪ =NORM.S.INV(1-alpha/2, TRUE)
o Margin of Error:
= ⁄2 √
o Confidence Interval: ̂ − < < ̂ + ̂ ̂ • Constructing Confidence Intervals for a Population Mean . o Best Point Estimate: ̅ o Critical Value: ⁄2 ▪ =T.INV(1-alpha/2, n-1, TRUE) o Margin of Error: = ⁄2 √ o Confidence Interval: ̅ − < < ̅ + • Constructing Confidence Intervals for a Population Standard Deviation . o Best Point Estimate: o Left Critical Value: 2 (Chi-squared left) ▪ =CHISQ.INV(alpha/2, n-1, TRUE) o Right Critical Value: 2 (Chi-squared right) ▪ =CHISQ.INV.RT(alpha/2, n-1, TRUE) o Confidence Interval: √ • ( − 1) 2 ( − 1) 2 √ < < 2 2 Finding Minimum Sample Size o For a Population Proportion ▪ If ̂ is known: 2 [ ⁄2 ] ̂ ̂ = 2 ▪ If ̂ is unknown: 2 [ ⁄2 ] . 25 = 2 o For a Population Mean ▪ When is known: =[ ▪ ⁄2 ∙ 2 ] When is unknown: =[ ⁄2 ∙ 2 ] STA3215 Course Project Phase 2 Our next phase of analysis will be to construct confidence intervals that will give us an estimated range of where the true average height of all of my family members lies. A confidence interval is defined as redacted. It is comprised of two components, a point estimate and a margin of error. A point estimate is a redacted. The best point estimate to use for a population mean is redacted. Confidence intervals are useful tools because redacted (instructor note: it is up to you find the information that goes in the redacted portions). Our first confidence interval will use a confidence level of 95%, that means we will use a value of = 0.05. The sample mean we found in phase 1 is: ̅ = 67.5758 . We find the critical value with the Excel formula: =T.INV(1 − ⁄2 , ) = T.INV(0.975, 32). Thus, we get the critical value of: ⁄2 = 2.0369 Next, we find the margin of error with the formula: = ⁄2 √ = (2.0369) 3.6489 √33 = 1.2938 And now we can find the upper and lower bounds of the confidence interval with the formula: ̅ − < < ̅ + 67.5758 − 1.2938 < < 67.5758 + 1.2938 66.2819 < < 68.8696 Therefore, we conclude that the true average height ( ) for my family is between 66.2819 inches and 68.8696 inches. Technically speaking, if we were to repeat this experiment with the same sample size we would expect the sample mean ( ̅ ) to be within this range 95% of the time. Now we will repeat this process but use a confidence level of 99%, so that changes our value of alpha to 0.01. The sample mean we found in phase 1 is: ̅ = 67.5758 . We find the critical value with the Excel formula: =T.INV(1 − ⁄2 , ) = T.INV(0.995, 32). Thus, we get the critical value of: ⁄2 = 2.7385 Next, we find the margin of error with the formula: = ⁄2 √ = (2.7385) 3.6489 √33 = 1.7394 And now we can find the upper and lower bounds of the confidence interval with the formula: ̅ − < < ̅ + 67.5758 − 1.7395 < < 67.5758 + 1.7395 65.8363 < < 69.3152 Therefore, we conclude that the true average height ( ) for my family is between 65.8363 inches and 69.3152 inches. Technically speaking, if we were to repeat this experiment with the same sample size we would expect the sample mean ( ̅ ) to be within this range 99% of the time. Upon review, we find that the redacted confidence interval is the wider of the two. This is because redacted (instructor note: it is up to you find the information that goes in the redacted portions). ... Purchase answer to see full attachment