Answer in Statistics and Probability for M_2 #247077

Maximum breadth of samples of male Egyptian skulls from 4000 B.C. and 150 A.D.

, based on data from Ancient Races of the Thebaid by Thomson and Randall-Maciver:

Don't use plagiarized sources. Get Your Custom Essay on
Answer in Statistics and Probability for M_2 #247077
Just from $13/Page
Order Essay

4000 B.C. : 131 119 138 125 129 126 131 132 126 128 128 131

150 A.D. : 136 130 126 126 139 141 137 138 133 131 134 129

Changes in head sizes over time suggest interbreeding with people from other regions.

Find the sample standard deviation and use a 90% confidence interval to determine

whether the head sizes appear to have changed from 4000 B.C. to 150 A.D. Explain your

result.

Since there is no information about the population, t – test is the most appropriate in finding the confidence interval for the difference in the means of the two samples. We use the difference in the means because it provides a better judgement when comparing groups.

Therefore, the 90% confidence interval is given by; the formula;

“\bar{x1}-\bar{x2} \pm” t“\alpha/2,v \sqrt{\frac{s1^2 }{n1} +\frac{s2^2}{n2}}” , where “\bar{x1}” ,“\bar{x2}” ,“s1^2” ,“s2^2” are the means and variances of the two random samples.

V is the degrees of freedom and is given by;

“(\frac{s1^2}{n1} + \frac{s2^2}{n2})^2” “/\frac{ (\frac{s1^2}{n1})^2}{n1-1} + \frac{(\frac{s2^2}{n2})^2}{n2-1}”

The degrees of freedom are calculated as above because we have unknown population variances that are assumed unequal.

From the data,

“\bar{x1}” = 128.6667 “\bar{x2}” = 133.3333

s1 = 4.63844 s2 = 5.015

n1 = 12 n2 = 12

“v =” “(\frac{4.63844^2}{12} + \frac{5.015^2}{12})^2 / \frac{(\frac{4.63844^2}{12})^2}{11} +\frac{ (\frac{5.015^2}{12})^2}{11}” = 21.8672

“\approxeq” 22

ta/2, v = t0.05 , 22 = 1.717

The 90% confidence interval is;

128.6667 – 133.3333 “\pm” 1.717 “\sqrt{\frac{4.63844^2}{12} + \frac{5.015^2}{12}}”

= (-4.6666“\pm” 3.3859)

= (-8.0525 , -1.2805)

Explanation of the results

From the confidence interval, we are 90% confident that the difference in the means of the two samples lies between -8.0525 and -1.2805.

Since the confidence interval does not include 0, we conclude that the head sizes of the male Egyptian skulls changed from 4000BC to 150AD,

and the difference is statistically significant

What Will You Get?

We provide professional writing services to help you score straight A’s by submitting custom written assignments that mirror your guidelines.

Premium Quality

Get result-oriented writing and never worry about grades anymore. We follow the highest quality standards to make sure that you get perfect assignments.

Experienced Writers

Our writers have experience in dealing with papers of every educational level. You can surely rely on the expertise of our qualified professionals.

On-Time Delivery

Your deadline is our threshold for success and we take it very seriously. We make sure you receive your papers before your predefined time.

24/7 Customer Support

Someone from our customer support team is always here to respond to your questions. So, hit us up if you have got any ambiguity or concern.

Complete Confidentiality

Sit back and relax while we help you out with writing your papers. We have an ultimate policy for keeping your personal and order-related details a secret.

Authentic Sources

We assure you that your document will be thoroughly checked for plagiarism and grammatical errors as we use highly authentic and licit sources.

Moneyback Guarantee

Still reluctant about placing an order? Our 100% Moneyback Guarantee backs you up on rare occasions where you aren’t satisfied with the writing.

Order Tracking

You don’t have to wait for an update for hours; you can track the progress of your order any time you want. We share the status after each step.

image

Areas of Expertise

Although you can leverage our expertise for any writing task, we have a knack for creating flawless papers for the following document types.

Areas of Expertise

Although you can leverage our expertise for any writing task, we have a knack for creating flawless papers for the following document types.

image

Trusted Partner of 9650+ Students for Writing

From brainstorming your paper's outline to perfecting its grammar, we perform every step carefully to make your paper worthy of A grade.

Preferred Writer

Hire your preferred writer anytime. Simply specify if you want your preferred expert to write your paper and we’ll make that happen.

Grammar Check Report

Get an elaborate and authentic grammar check report with your work to have the grammar goodness sealed in your document.

One Page Summary

You can purchase this feature if you want our writers to sum up your paper in the form of a concise and well-articulated summary.

Plagiarism Report

You don’t have to worry about plagiarism anymore. Get a plagiarism report to certify the uniqueness of your work.

Free Features $66FREE

  • Most Qualified Writer $10FREE
  • Plagiarism Scan Report $10FREE
  • Unlimited Revisions $08FREE
  • Paper Formatting $05FREE
  • Cover Page $05FREE
  • Referencing & Bibliography $10FREE
  • Dedicated User Area $08FREE
  • 24/7 Order Tracking $05FREE
  • Periodic Email Alerts $05FREE
image

Our Services

Join us for the best experience while seeking writing assistance in your college life. A good grade is all you need to boost up your academic excellence and we are all about it.

  • On-time Delivery
  • 24/7 Order Tracking
  • Access to Authentic Sources
Academic Writing

We create perfect papers according to the guidelines.

Professional Editing

We seamlessly edit out errors from your papers.

Thorough Proofreading

We thoroughly read your final draft to identify errors.

image

Delegate Your Challenging Writing Tasks to Experienced Professionals

Work with ultimate peace of mind because we ensure that your academic work is our responsibility and your grades are a top concern for us!

Check Out Our Sample Work

Dedication. Quality. Commitment. Punctuality

It May Not Be Much, but It’s Honest Work!

Here is what we have achieved so far. These numbers are evidence that we go the extra mile to make your college journey successful.

0+

Happy Clients

0+

Words Written This Week

0+

Ongoing Orders

0%

Customer Satisfaction Rate
image

Process as Fine as Brewed Coffee

We have the most intuitive and minimalistic process so that you can easily place an order. Just follow a few steps to unlock success.

See How We Helped 9000+ Students Achieve Success

image

We Analyze Your Problem and Offer Customized Writing

We understand your guidelines first before delivering any writing service. You can discuss your writing needs and we will have them evaluated by our dedicated team.

  • Clear elicitation of your requirements.
  • Customized writing as per your needs.

We Mirror Your Guidelines to Deliver Quality Services

We write your papers in a standardized way. We complete your work in such a way that it turns out to be a perfect description of your guidelines.

  • Proactive analysis of your writing.
  • Active communication to understand requirements.
image
image

We Handle Your Writing Tasks to Ensure Excellent Grades

We promise you excellent grades and academic excellence that you always longed for. Our writers stay in touch with you via email.

  • Thorough research and analysis for every order.
  • Deliverance of reliable writing service to improve your grades.
Place an Order Start Chat Now
image