Question

an 25 A pharmacologist decided to test two common headache-tables for the effectiveness: Tablet A Scomg and Tablet B20 mg. The experiment was conducted as follows: A random patient that walked into the dini and complained of a headache was genether tablet A tablet or a placebo. After swallowing the tablet the patient was asked to stay in the dinik for an hour and afterwards to report whether the headache had disappeared improved, or the tablet had no effect fe no improvement or even a worsening of the headache nters Use a 14 level of significance to test the claim that headache status is independent of headache relief tablet used, Headache Desappeared Headache improved Chane Total Tablet A 10 10 hoo frablet bo 10 20 Pacebo 50 hos Total 1190 25 bos Contingency Tablet Hypotheses Ho Headache status is independent of headache relictablatused H:Headache status is dependent on headache relief tablet used. Expected Values Complete the table of expected outcomes fround values to 3 decimal places Headache Disappeared Headache improved No Change Tablet Tablet 16.780 Placebo 67627 Results Calculate the test statistic use two decal places Y- State the p-value (round to the nearest hundredth of a percent. 1.53) P-value Conclusion We sufficient evidence to support the claim that patient headache status is dependent on which headache relatabiat was used to (Use "hove or tack for the first blank and for the second blank) 0.011

Answer 1

Disappeared Improved No change Total Tablet A 80 10 10 100 Tablet B 60 10 20 90 Placebo 50 30 25 105 Total 190 50 55 295 The expected values are computed in terms of row and column totals. In fact, the formula is Eij Rixc, where Ri corresponds to the total sum of elements in rowi, C; corresponds to the total sum of elements in column j, and T is the grand total. The table below shows the calculations to obtain the table with expected values: Expected Values Disappeared Improved No change Total Tablet A 190 x 100 205 64.407 50x100 295 16.949 55 x 100 295 18.644 100 Tablet B 190 x 90 295 = 57.966 50x90 295 = 15.254 55 x 90 295 = 16.78 90 Placebo 190 x 105 295 = 67.627 50 x 105 = 17.797 55 x 105 295 = 19.576 105 205 Total 190 50 55 295 Based on the observed and expected values, the squared distances can be computed according to the following formula: (E-0)?/E. The table with squared distances is shown below: Squared Distances Disappeared Improved No change Tablet A (80–64.407) 64.407 (10-16.949) = 3.775 = 2.849 (10-18,644) 18.644 = 4.008 16.949 Tablet B (60-57.966) 57.966 = 0.071 (10-15.254) 15.254 = 1.81 (20-16.78) 16.78 = 0.618 Placebo (50-67.627) 67.627 = 4.595 (30-17.797) 17.797 = 8.368 (25-19.576) 19.576 = 1.503

Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: Headache status is independent to headache relief Tablet used H1: Headache status is dependent to headache relief Tablet used This corresponds to a Chi-Square test of independence. Rejection Region Based on the information provided, the significance level is a = 0.01, the number of degrees of freedom is df = (3 – 1) (3-1) = 4, so then the rejection region for this test is R = {x? : x² > 13.277). Test Statistics The Chi-Squared statistic is computed as follows: (Oi; – E;;) Ejj = 3.775 +0.071 + 4.595 +2.849 + 1.81 +8.368 + 4.008 + 0.618 + 1.503 = 27.597 i=1 Decision about the null hypothesis Since it is observed that x? hypothesis is rejected. = 27.597 > xã = 13.277, it is then concluded that the null Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that Headache status is dependent to headache relief Tablet used The corresponding p-value for the test is p= Pr(xả > 27.597) = 0.

TR Console > P.Value=1-pchisq (27.597,4) (1) 1.505238e-05 > 1