# 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:

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Answer in Statistics and Probability for M_2 #247077
Just from $13/Page 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. #### 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. # 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

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