Question

1. Based on the sample, the 95% confidence interval for the blood level of inorganic phosphorous is (1.153, 1.247). Which one of teh following statements is a correct interpretation of this interval? A. If we took 100 additional samples of the same size and from each compute a 95% confidence interval, 95 of the intervals are identical to (1.153, 1.247). B. There is a 95% chance that the sample average inorganic phosphorus level of a random sample of 12 healthy elderly subjects is in between 1.153 mmol/l and 1.247 mmol/l. C. We are 95% confident that the true mean phosphorous level is in between 1.153 and 1.247 mmol/l. D. There is a 95% chance that the true mean phosphorous level is in between 1.153 mmol/l and 1.247 mmol/l.

2. In Sharon Woods Park, a biologist is trapping chipmunks to study their population. Let A be the event that the chipmunk is male and B be the event the chipmunk is pregnant. Which of the following is true about A and B? A. A and B are independent B. P(A) = 1- P(B) C. All of the given options are true. D. P(A or B) = P(A) + P(B)

3. Hodgkin lymphoma is one of the most curable forms of cancer. The five-year survival rate for this cancer is 72%. If three unrelated (independent) patients are newly diagnosed with Hodgkin lymphoma, the probability that none of the three survive for five years is 0.022. What is the probability that at least one survives for five years? A. 0.72 B. 0.76 C. 0.978 D. 0.575

Answer 1

1. Correct option :  C. We are 95% confident that the true mean phosphorous level is in between 1.153 and 1.247 mmol/l.

Reason : A 95% confidence interval is a range of values that you can be 95% certain contains the true mean of the population.

2. Correct option : D. P(A or B) = P(A) + P(B)

Reason : We know that, P(A or B ) = P(A) + P(B) - P(A and B)

Since events A and B are mutually exclusive, P(A and B ) = 0

So, P(A or B ) = P(A) + P(B)

3. Correct option : C. 0.978

Reason : We know that  probability that none of the three survive for five years = 0.022

So, probability that at least one survives for five years = 1 - probability that none of the three survive for five years

= 1 - 0.022 = 0.978