Question

(1 point) Archeologists have discovered a sample of ancient Egyptian skulls from 4000 B.C. A sample of 6 Egyptian skull breadth (in mm) from 4000 B.C. is show below: Skull breadth Sample: 123, 128, 136, 133, 135, 119 (a) Calculate the mean and standard deviation for for the data set. Round the mean to 2 decimal places, and the standard deviation to 4 decimal places 4000 B.C. skull breadths mean: 4000 B.C. skull breadths standard deviation: (b) Using your answers from part (a) and the formula for a 99% confidence interval as presented in lecture, fill in the blanks with the appropriate values for this problem for calculating the confidence interval below. To enter a where x is any number, type sqrt(x). For example, V2 should be written as sqrt(2). 4000 B.C. skull breadths: to (c) Using the formulas from part (b), find the 90% confidence intervals for the mean maximum skull breadths of all Egyptian skulls from 4000 B.C. Round your answer to the nearest hundredth (2 decimal places). 4000 B.C. skull breadths: to

Answer 1

Solution: The provided sample of 6 Egyptisao skull breadths from 4000 Bc. is shown below. 123 128,136, 133, 135,119 Calculate the mean for the data seda and standard deviation We know that: Mean = ² = 11 123+1284 136 + 133+135 +119 6 774 6 = Mean X 129 4000 13.c. Skell breadths mean: 129 We know that, Sample standard deviation sa 3(x-7) ² - nal

consider &li-x2² 11 (123-129)?+(128-129) ?+ (136 - 129) ? + (133-129) ?+ (135-129) ?+ (119-129) 238 Sample standand devicetos so 238 6-1 6.8993 4000 3.5. skuell bocadith standard deviation 6.899.3. b) using your your answers from part (a) and the formula for a 99% confidence internal as presented in lecture, fill in the blocks with the apprepnisite calces for the problem for calcubbing the confidence intral below. lale know that the confidence internal for population mean is given cos's

CIE X - to XS xt texs sqrt(n) sext(o) Here x = 129 sa 6.8993 6 to. i.e. t critical value. To find

The qumber of degrees of freedom cits df = Orla G-175 and the significance level is Cool Based on the provided Lo formation the cntical tt-value for año.ol and dfas degrees of freedom is Is40032 (129- 4.032x 6.8993_1294 4.032x 6.8993 sext) sqrt(6) 4000 13.6. skull breadths's Foto 129-41032% 6.8993 saato) to lag+ 4.632 x 6.8993 Sente) c) using the formules from proti bo find the got Confidence internets for the mean maximum skull bocadths of all fissyptisce skeells him 4.000 B:C ci: 129-4-032. * 6.1993 Syst (6) 12 9 to 4*032 X6.8993 sqat (6) & 129 129 - 11.357 117.643 117.69 to 129 af 11.357 to 140.357 to 140. 36 4000 B.C.skull breast this: 119.64 to 140.36.