In this exercise , a two-way table is shown for two groups , 1 and 2 , and two possible outcomes , A nad B begin{array}{|c|c|c|}hline &text{Outcome A}

tricotasu

tricotasu

Answered question

2020-10-26

In this exercise , a two-way table is shown for two groups , 1 and 2 , and two possible outcomes , A nad B Outcome AOutcome BTotalGroup 1302050Group 240110150Total70130200
a) What proportion of all cases had Outcome A?
b) What proportion of all cases are in Group 1?
c) What proportion of cases in group 1 had Outcome B?
d) What proportion of cases who had Outcome A were in group 2?

Answer & Explanation

curwyrm

curwyrm

Skilled2020-10-27Added 87 answers

Step 1
Solution:
The two way table is
Outcome AOutcome BTotalGroup 1302050Group 240110150Total70130200
Step 2
a) The proportion of all cases had outcome A is P(A)=70200=0.350
The proportion of all cases had outcome A is 0.350
b) The proportion of all cases in Group 1 is P(G1)=5200=0.250
The proportion of all cases in Group 1 is 0.250
c) To find the proportion of cases in group 1 had outcome B that is to find the proportion of outcome B given that in group 1
P(BG1)
P(BG1)=P(BG1)P(G1)
P(BG1)=2050=0.400 The proportion of cases in group 1 had outcome B is 0.400
d) To find the proportion of cases who had outcome A were in group 2 that is to find the proportion of outcome a given that in group 2 P(AG2)
P(AG2)=P(AG2)P(G2)
P(AG2)=40150=0.266667
P(AG2)=0.267
The proportion of cases who had outcome A were in group 2 is 0.267

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