Question

• 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.

4. 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.

The data for this is the graduation rates spread across 50 states. The analysis will contain 50 data pieces. They are provided below:

• Alabama 89.3%
• Alaska 78.2%
• Arizona 78%
• Arkansas 88%
• California 82.7%
• Colorado 79.1%
• Connecticut 87.9%
• Delaware 86.9%
• Florida 82.3%
• Georgia 80.6%
• Hawaii 82.7%
• Idaho 79.7%
• Illinois 87%
• Indiana 83.8%
• Iowa 91%
• Kansas 86.5%
• Kentucky 89.7%
• Louisiana 78.1%
• Maine 86.9%
• Maryland 87.7%
• Massachusetts 88.3%
• Michigan 80.2%
• Minnesota 82.7%
• Mississippi 83%
• Missouri 88.3%
• Montana 85.8%
• Nebraska 89.1%
• Nevada 80.9%
• New Hampshire 88.9%
• New Jersey 90.5%
• New Mexico 71.1%
• New York 81.8%
• North Carolina 86.6%
• North Dakota 87.2%
• Ohio 84.2%
• Oklahoma 82.6%
• Oregon 76.7%
• Pennsylvania 86.6%
• Rhode Island 84.1%
• South Carolina 83.6%
• South Dakota 83.7%
• Tennessee 89.8%
• Texas 89.7%
• Utah 86%
• Vermont 89.1%
• Virginia 86.9%
• Washington 79.4%
• West Virginia 89.4%
• Wisconsin 88.6%
• Wyoming 86.2%

Successfully compute the computational problems above the sample set for completion of this post. Thank you for your help!

Answer 1

mean	0.84742
sample standard deviation	0.04320
confidence interval 80.% lower	0.83948
confidence interval 80.% upper	0.85536
margin of error	0.00794
t(df = 49)	1.299
confidence interval 95.% lower	0.83514
confidence interval 95.% upper	0.85970
margin of error	0.01228
t(df = 49)	2.01
confidence interval 99.% lower	0.83105
confidence interval 99.% upper	0.86379
margin of error	0.01637
t(df = 49)	2.68
confidence interval 90.% lower	0.83718
confidence interval 90.% upper	0.85766
margin of error	0.01024
t(df = 49)	1.677

The mean and standard deviation of your sample are 0.84742 and 0.04320 respectively.

The 80% confidence interval is between 0.83948 and 0.85536 with a margin of error 0.00794.

The 95% confidence interval is between 0.83514 and 0.85970 with a margin of error 0.01228.

The 99% confidence interval is between 0.83105 and 0.86379 with a margin of error 0.01637.

The 90% confidence interval is between 0.83718 and 0.85766 with a margin of error 0.01024.

We can observe that as the confidence interval increases, the width of the confidence interval increases.

The margin of error increases as the confidence level increases.