The Hoffman family has bought one pizza on Friday night every week for the last 10 years.
1 answer:
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Answer: a. A point estimate for p is 0.597 .
b. The 95% confidence interval for p.
Lower limit = 0.48
Upper limit = 0.71
Step-by-step explanation:
Given : Sample size of professional actors : n= 67
Number of extroverts : x= 40
Let p represent the proportion of all actors who are extroverts.
a. The point estimate for p = sample proportion =
b. Confidence interval for population proportion :
Since the critical value for 95% confidence interval is 1.96 , so the 95% confidence interval for p would be
In the 95% confidence interval for p.
Lower limit = 0.48
Upper limit = 0.71
Answer:
93.25% probability that they have taken this steroid
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Positive test
Event B: Taking the steroid.
Suppose the probability of an athlete taking a certain illegal steroid is 10%.
This means that
Given that the athlete has taken this steroid, the probability of a positive test result is 0.995.
This means that
Positive test:
99.5% of 10%(If the athlete has taken).
100-99.2 = 0.8% of 100-10 = 90%(Athlete has not taken)
Then
Given that a positive test result has been observed for an athlete, what is the probability that they have taken this steroid
93.25% probability that they have taken this steroid