x (chord length in mm) 78 75 y (capacity in cm³) 850 775 7550 81 84 86 87 975 915 1015 1030 2x = 569 Ey=6310 Suppose that from previous evidence, anthropologists had believed that for each 1-mm increase in chord length, cranial capacity would be expected to increase by 20 cm³. Do these new experimental data strongly contradict prior beliefs? State your hypotheses, calculate your test statistic, p value and interpret your results. Use a 5% alpha level and assume all the basic assumptions are met. a) Ho: Ha: = ẞ slope of population regression line relating cranial capacity in cm³ to chord length in mm. b) Because ẞ is not = 0, you cannot use the built-in hypothesis test with your calculator. Do the basic calculations manually with your calculator. Fill in the values below that are needed to do this calculation. I put in the formulas to assist you. Show 4 decimals for all the values below. Use your calculator to calculate the regression equation ŷ = ax + b Write your equation here. a = slope = stal Calculate Se= Calculate Sx = Fill in values here for t test statistic. Calculate √√Sxx =√n-1 sx = Se Calculate Sa= wolsa-ß t = = Sxx Sa Test Statistic value: 4 dec What df do you use? c) Calculate the P value by rounding your test statistic above to 1 decimal place before looking up your value in the tables provided. Note that this is a two tailed test as you complete the calculation below. The p-value is (fill in the blanks) _x P(t> X (p-value) 1 dec. table value 3 dec. d) Interpret your results: (p-value vs alpha, reject/fail to reject Ho) Nothing else is needed here. 2) In anthropological studies, an important characteristic of fossils is cranial capacity. Frequently skulls are at least partially decomposed, so it is necessary to use other characteristics to obtain information about capacity. One such measure that has been used is the length of the lambda opisthion chord. The article "Vertesszollos and the Presapiens Theory" (American Journal of Physical Anthropology [1971]) reported the accompanying data for n = 7 Homo erectus fossils.