Question

On average is the younger sibling's IQ lower than the older sibling's IQ? Ten sibling pairs were given IQ tests. The data are shown below. IQ Scores Younger Sibling 106 85 91 113 91 110 96 96 87 116 Older Sibling 109 83 91 126 85 111 98 107 91 122 Assume a Normal distribution. What can be concluded at the the a= 0.10 level of significance? For this study, we should use Select an answer a. The null and alternative hypotheses would be: Ho: Select an answer Select an answer (please enter a decimal) H: Select an answer ? Select an answer (Please enter a decimal) b. The test statistic ? (please show your answer to 3 decimal places.) c. The p-value (Please show your answer to 4 decimal places.) d. The p-value is e. Based on this, we should Select an answer the null hypothesis. f. Thus, the final conclusion is that va

Answer 1

• Here we use T-Test for 2 Independent Means

Younger sibling older sibling & (xi-M₃) 2 (Yi-My 12 log 83 91 106 85 91 113 91 110 96 96 87 116 126 85 111 98 107 91 122 47.61 198.81 65.61 193.21 65.61 118.81 9.61 9.61 146.41 285.61 44.83 372.49 127.69 56169 299.29 75.69 18. ug 22.09 127.69 388.09 10 10 Ex=gg1 Syi=1023 SS-1140.90 ssy=2038. 1 = 1023 = 102.3 ; S = 1 x SS, = 126.77 Mx991–99.1 10 S? 226.46 N N2 a) Ho: Mx My SSy = N₂ 1 H,: My > Mx (N = N2=10) 6 Mx, - My (N-15% +(N-1)} N,+N2-2 t = 1023-99.) 0.543 [to +7 $degree of pureedom =df df = N TN2-2 P-value far above t-scare can af =18 be calculated by using it-table for deque of praedoln =18 P-value = 0.2984 (d p-value a we accept nell X 9x1146.90+ 9x2038.1 lot 16-2 10 at x= 0.1 so hypothesis.