Question

4. The Centers for Disease Control and Prevention wants to determine if the severity of a skin disease is related to the age of the patient. Suppose that a patient's skin disease is classified as moderate, mildly severe, or severe. The patients are divided into four age categories. The data is as follows. Age Category II III IV I Severity Moderate Mildly Severe Severe 15 8 32 29 20 18 23 25 5 18 22 Total 70N 78 68 Total 24 81 66 45 216 Determine if there is a relationship between severity of skin disease and age of the patient.

Answer 1

Given. table- Age Category I IV 18 I 15 @ severity Moderate Miklly severe 5 T 32 29 20 81 Total 70 78 23 18 j 25 Severe Total 22 45 24 .66 216 . relationship 7-78 216 Null hypothes is Ho. There is not between severity of skin disease and age of_the_patient. Alternative Hypothesis H. There is relationship between severity of skin disease and age of the patient. Expeeted values valuies - E(15) = 24x70 E(32) = 81870 -26:25, F (18)= 66 x70_21-39, E(5)=-45470_14:58 216 216 E(8)=24x79-0-0.54 E(29) = 81x78_29.25€(23)=66X78_23183 216 216 E(18)=45878–16.25, E. (1) 22486.2_ 7.56 E (20) =81X68_25-50 216 216 216 E(25) = 66X68__20.78, E (22)= 452682 14:17. 216 216 chi-square value E O-E)? 92= (15-7.78127 +622-14.17)2 27.135 14.17 216 216 E 7.78

det level of significance is 2-0.05. degree of freedom's = (K-1 (8-1) = (4-1)(3- S6 P-value for chi-square & chi-square ² = 27.135 df = 6 from p-value table is = 0.0ool Since P-value is less than the level of significance. then Reject the nult hypothesis at ZO.05 evidence a relationship There is sufficient to conclude that there is between severity of skin disease and age of patient.