Question

Weights of 50 babies at birth.

Write at least a 1-Page Report Open a Word Document

Introduction--Provide a description of your topic and cite where you found your data. Sample Data—Include a 5x10 table including your 50 values in your report. You must provide ALL of your sample data.

Problem Computations—For the topic you chose, you must answer the following: Determine the mean and standard deviation of your sample. Find the 80%, 95%, and 99% confidence intervals. Make sure to list the margin of error for the 80%, 95%, and 99% confidence interval. Create your own confidence interval (you cannot use 80%, 95%, and 99%) and make sure to show your work. Make sure to list the margin of error.

Problem Analysis—Write a half-page reflection. What trend do you see takes place to the confidence interval as the confidence level rises? Explain mathematically why that takes place. Provide a sentence for each confidence interval created in part c) which explains what the confidence interval means in context of topic of your project. Explain how Part I of the project has helped you understand confidence intervals better? How did this project help you understand statistics better?

Answer 1

Answer:

Given Data

The percent change in personal Income Across 50 States 2019.

WA 7.0%	NM 6.1%	AR 5.0%	AL 4.9%	NJ 5.3%
OR 6.2%	ND 0.0%	LA 4.9%	FL 6.0%	PA 5.4%
CA 5.8%	SD 1.3%	WI 4.4%	GA 4.8%	NY 6.0%
ID 7.4%	NE 3.6%	IL 4.2%	SC 5.6%	CT 4.8%
NV 6.3%	KS 3.9%	MI 5.1%	NC 5.6%	RI 4.6%
AZ 6.3%	OK 3.4%	IN 3.9%	VA 5.7%	MA 3.8%
UT 6.9%	TX 7.5%	OH 4.5%	WV 4.0%	ME 4.9%
MT 5.9%	MN 5.2%	KY 4.0%	DC 5.6%	NH 4.4%
WY 6.0%	IA 2.3%	TN 5.0%	MD 4.9%	VT 5.0%
CO 4.8%	MO 4.6%	MS 3.3%	DE 6.2%	AK 5.6%

Calculate the mean , standard deviation and confidence intervals for the above sample data

i) For 95% confidence interval (CI) we have = 0.05 & the 95% CI is  

where ,

   Sample mean

   Standard deviation of the data

n = sample size

Mean of the data

= 5.912

Standard deviation =   

= 6.936

So 95% is  

=  

= ( 3.9894 , 7.8346)

Margin of error =

=  

= 1.9226

ii) The 80% CI can be calculated by using = 0.20

80% CI is

= ( 4.6564 , 7.1676 )

Margin of error

=

= 1.2556

iii) For 99% CI we have   = 0.01

  

= ( 3.3813 , 8.4427 )

Margin of error = 2.5307

Now we create a 90 % CI by using = 0.1

90% CI is

=  

= ( 4.3033 , 7.5207 )

Margin of error = 1.6087

iv) Problem analysis:

We see that 80% CI is ( 4.6564 , 7.1676 )

90% CI is (4.3033 , 7.5207 )

95% CI is ( 3.9894 , 7.8346 )

99% CI is ( 3.3813 , 8.4427 )

Pictorially we have

We see confidence level increases ( from 80% to 99% ) the size or length of the CI increases.

So , that concludes if we repeat an experiment 100 times , 80% of the time it will fall in the interval ( 4.6564 , 7.1676 ) & 99% of time ( 3.3813 , 8.4427 )

Also, the margin of error increases as the confidence level increases.

For each of the confidence level we get an idea about how the percent change in persinal income Across 50states in 2019 took place. At 80% level we can say percent change lies in the interval ( 4.6564 , 7.1676 ) & so on.

Importance of the project to know more about CI:

The project helped using different level of confidence levels & how they influence the intervals.

To know more about Statistics:

Confidence intervals are about rist . They consider the sample size & the potential variation in the population & give us an estimate of the range in which the real answer lies. So when exact answers are not obtainable , confidence intervals helps a lot to get an idea of the value & its neighborhood.

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