1) A system may make two types of errors. Let A denote the event that the system

Question

1) A system may make two types of errors. Let A denote the event that the system makes a type 1 error, and B denote the event that the system makes a type 2 error. Suppose that the probability of the system making either type of error is the same (that is P(A) = P(B)). Moreover, assume that the probability of the system making at least one type of error is 0.36. Then which of the following statement is correct:

a) If A and B are disjoint, then P(A)=0.6

b) If A and B are disjoint, then P(A)=0.18

c) If A and B are independent , then P(A)=0.6

d) If A and B are independent , then P(A)=0.18

2) Total cholesterol levels were measured in a random sample of 500 men, and the resulting 95% confidence interval for the mean was (173.1, 177.1). Indicate which of the following interpretations is correct:

a) 95% of the men in the sample had total cholesterol levels between 173.1 and 177.1.

b) The probability that the true mean total cholesterol level for men lies between 173.1 and 177.1 is 0.95.

c) If we computed similar confidence intervals based on many random samples of 500 men, approximately 95% of them would contain the population mean total cholesterol level for men.

d) The confidence interval does not contain 0, so we reject the null hypothesis.

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Explanation / Answer

1) Given,

P(At least one type of error) = 0.36

So,

P(A or B) = 0.36

Assuming these events to be disjoint,

P(A) + P(B) = 0.36

Given,

P(A) = P(B)

So,

2 P(A) = 0.36

P(A) = 0.18

Option B is correct.

2. Option C is correct.

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