4.2 Stats HW

Which of the following is NOT a principle of​ probability?

All events are equally likely in any probability procedure.

classical approach to probability.

If the outcomes are not equally​ likely, we cannot use the classical approach to probability.

sample space

for a procedure consists of all possible simple events. That​ is, the sample space consists of all outcomes that cannot be broken down any further.

In a clinical trial of 2042 subjects treated with a certain​ drug, 21 reported headaches. In a control group of 1703 subjects given a​ placebo, 21 reported headaches. Denoting the proportion of headaches in the treatment group by pt and denoting the proportion of headaches in the control​ (placebo) group by pc​, the relative risk is pt​/pc. The relative risk is a measure of the strength of the effect of the drug treatment. Another such measure is the odds​ ratio, which is the ratio of the odds in favor of a headache for the treatment group to the odds in favor of a headache for the control​ (placebo) group, found by evaluating (pt/(1-pt))/(pc/(1-pc)). The relative risk and odds ratios are commonly used in medicine and epidemiological studies. Find the relative risk and odds ratio for the headache data. What do the results suggest about the risk of a headache from the drug​ treatment?

o find the relative risk for the headache​ data, first calculate the proportion of headaches in the treatment group. pt equals= number of subjects who reported headaches in the treatment group / total number of subjects in the treatment group 21/2042 =.0103 Then calculate the proportion of headaches in the control group 21/1703 = .0123 Now calculate the relative risk using the formula given in the problem statement. pt / pc .0103 / .0123 = .837 To find the odds​ ratio, first calculate the odds in favor of a headache for the treatment group Pt/1-Pt .0103 / 1-.0103 = .0104 Then calculate the odds in favor of a headache for the control group Pc/1-Pc .0123 / 1-.0123 = .0125 Now calculate the odds ratio using the formula given in the problem statement. (pt/(1-pt))/(pc/(1-pc)) .0104 / .0125 = .832 What do the results suggest about the risk of a headache from the drug​ treatment? Compare the proportion pt of a headache with the drug to the proportion pc of a headache with the placebo. The drug does not pose a risk of headaches as long as pt is less than than pc.

The payoff odds against event A represent the ratio of net profit​ (if you​ win) to the amount bet.

payoff odds against A=​(net ​profit):(amount bet) a:b 15/32 and 17/32 15:17

law of large numbers

procedure is repeated again and​ again, the relative frequency of an event tends to approach the actual probability