Question

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4. A researcher wishes to see if there is a relationship between the hospital and the number of patient infections. A sample of 3 hospitals was selected, and the number of infections for a specific year has been reported. The data are shown next. Hospital Total A B с Total Surgical site Infections 41 36 169 246 Pneumonia infections 27 3 106 136 Bloodstream Infections 51 40 109 200 119 79 384 582 At a = 0:05 can it be concluded that the number of infections is related to the hospital where they occurred?

Answer 1

observed frequency table: Surgical site Pneumonia infections infections А 41 27 B 36 3 с 169 106 Bloodstream infections 51 40 109 Expected frequency table: (Row total)*(Column total) Expected frequency Grand Total A Surgical site infections 50.0 33.0 162.0 Pneumonia infections 28.0 18.0 90.0 Bloodstream infections 41.0 27.0 132.0 B с The null and alternative hypothesis: Ho : Number of infection and hospital where they occurred are independent. H1 : Number of infection and hospital where they occurred are dependent. Test statistc: (Observed frequency - Expected frequency) 42 X2 = E( .) Expected frequency = 30.6962 The test statistc is 30.6962

Rejection Criteria : row = total number of rows = 3 column = total number of columns = 3 degrees of freedom = (row-1)*(column-1) degrees of freedom = (3-1)*(3-1) degrees of freedom = 4 = 0.05 level of significance = alpha critical value =9.4877 p-value = 0.0 Reject Ho: a) If abs(test statistic) >= critical OR b) If p-value <= alpha Decision:a) Based on critical value: Reject He, since ( abs(test statistic) = 30.6962) >= (critical = 9.4877) b) Based on p-value: Reject He, since (p-value = 0.0) <= (alpha=0.05) Conlusion .There is sufficient evidence to conclude that Number of infection and hospital where they occurred are related.