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Question: Amongst a group of patients who complained of severe body pain, some were given a new analgesic on trial and some were given a placebo. They were later asked whether the pain relievers were effective. The results were presented in the following table. Pain relieved Pain continues Took analgesic 90 20 Took placebo 40 170
Assuming that they spoke the truth, find the chi-square test value and test the hypothesis that there is no difference between the pain relieving analgesics and placebo at a significance level α Steps to derive 1 H0 : There is no difference between analgesics and placebos in relieving pain.1 : Analgesics were effective in relieving pain.2 The degrees of freedom is (2 - 1) × (2 - 1) = 1. The critical value for α 3 Pain relieved Pain continues Total Took analgesic 90 20 110 Took placebo 40 170 210 Total 130 190 320
4 The expected frequencies are computed as follows:Pain relieved Pain continues Total Took analgesic 1 1 0 × 1 3 0 3 2 0 1 1 0 × 1 9 0 3 2 0 110 Took placebo 2 1 0 × 1 3 0 3 2 0 2 1 0 × 1 9 0 3 2 0 210 Total 130 190 320
R o w s u m × C o l u m n s u m G r a n d t o t a l 5 The completed table is presented below with the expected frequencies, shown within brackets:Pain relieved Pain continues Took analgesic 90(44.69) 20(65.31) Took placebo 40(85.31) 170(124.69)
6 c 2 = ∑ ( O - E ) 2 E 7 c 2 = ( 9 0 - 4 4 . 6 9 ) 2 4 4 . 6 9 ( 2 0 - 6 5 . 3 1 ) 2 6 5 . 3 1 ( 4 0 - 8 5 . 3 1 ) 2 8 5 . 3 1 ( 1 7 0 - 1 2 4 . 6 9 ) 2 1 2 4 . 6 9 8 c 2 = 45.94 + 31.43 + 24.06 + 16.47 = 117.99 Since 117.9 > 3.84, the decision is to reject the null hypothesis.10 The analgesics were more effective in relieving pain.Hence the right answer is Option A Click Here To Go Back What is the value of (- 321) + 77?.. Find the sum.0 + (- 7).. What is the value of 4 + (- 8)?.. What is the value of (- 82) + 2?.. What is the value of 3 + (- 7)?.. Find the value of 7 + (- 5) + (- 3)... Find the sum.- 9 + 17.. Find the value of - 6 + 2... Find the sum.- 5 + 12.. The temperature of a juice in a refrigerator is - 9°C. When it is taken out from the r.. What is the value of 8 - 2?.. What is the value of - 5 - (- 7)?.. What is the value of - 1 - 9?.. What is the value of 27 - (- 6)?.. What is the value of the expression - 50 - (- 14)?.. 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