Question

State the hypotheses and identify the claim, find the critical value(s), compute the test value, make the decision, summarize the results (make the appropriate statement of the results of the claim included rejection of non rejection of the null hypothesis). Please show ALL work. DO NOT USE THE P VALUE. Please include a bell graph.

Is there a significant difference at a=0.10 in the average height in feet of high towers in Europe and the ones in South Africa? The data are shown.

Europe

497 1236 1288 463 1312 987 888 365

South Africa

714 705 964 1227 325 830 369 721 1799

Answer 1

Solution Europe South Africa 497 714 705 1236 1288 964 463 1227 1312 325 987 830 369 888 365 721 1799 Total 7036 7654 n 8 Mean 879.5 850.4444 Variance 153876.9 202409 S.D 392.2714 44 9.8989 Let the two independent small samples of sizes n, & na be 112, xin, & 221, 222, ..22n, resp. The test statistic for testing; Ho: el - M₂ = vų HI: M-12 0 Here, 6.2 & 2² t-test for Ho can be performed using W. G. Cochran's approximate t-test. Statistic under Cochran's approximate test is. t = X - X SI ni + S2 na

For making a decision about Ho vis-a-vis Hi, calculated is compared with tt. value of t Where, t* 2 S. x ta,n,n & S2² x tx, na-1 in + S2² ni 12 Reject Ho if tt *; otherwise accept Ho. Here, n = 8,24 879.5, S1² = 153876.9 to 1,7 = 1.4149 12 -9, M = 850.4444 S₂ = 20240g, to.1,8= 1.3968 Test statistic is, Critical region ta - H2 reject to at Accept Ho n2 29.0556 2.04.2657 -00 O 1.405) 0.1422 Critical value for t-statistic, t* = 5,² x ta, n, 1 + S2² x to, n₂-1 n na 5,2 + S2² nz 19234.6125 X 1.4149 +22489.8889 x 1-3968 19234.6125 + 22499.8899 1-4051 no Here, tat*, hence accept Ho. ie. there is significant difference differente in average height of high towers at a = 0.10 1.0.5.