The results of the study are presented in the table below. Significant Reduction in Pain? Type...
The results of the study are presented in the table below.
Significant Reduction in Pain? Type of Injection NO YES Total SALINE 19 3 22 BOTOX 11 10 21 Total 30 13 43
7. What is the probability a patient in this experiment had a significant reduction in pain? Write the fraction and the decimal. Round the decimal to two places. P(YES) =
8. What is the probability a patient has a Botox injection AND had a significant reduction in pain? Write the fraction and the decimal. Round the decimal to two places. P(BOTOX and YES) =
9. What is the probability that a randomly selected patient that received a saline injection had a significant reduction in pain? Write the fraction and the decimal. Round the decimal to two places. P(YES | SALINE) =
10. What is the probability that a patient who received a Botox injection had a significant reduction in pain? Write the fraction and the decimal. Round the decimal to two places. P(YES | BOTOX) =
11. Are the type of injection and having a significant reduction in pain independent or dependent? Explain your answer.
12. Are having a saline injection and having a significant reduction in pain mutually exclusive?
Homework Answers
7) Probability that a patient in this experiment had a significant reduction in pain , P(YES) = 13/43 = 0.30
8) P(BOTOX and YES) = 10/43 = 0.23
9) P(YES | SALINE) = P(YES and SALINE)/P(SALINE) = 3/22 = 0.14
10) P(YES | BOTOX) = P(YES and BOTOX)/P(BOTOX)
= 10/21 = 0.48
11) P(significant reduction in pain and type of injection as SALINE)
= P(YES and SALINE) = 3/43 = 0.07
P(YES)*P(SALINE) = 13/43 * (22/43) = 0.15
Since, these are not equal .The type of injection and having a significant reduction in pain is dependent.
12) Since, P(SALINE and YES) = 0.07 which is not equal to 0, thus these are not mutually exclusive.
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