| № |
Condition |
free/or 0.5$ |
| m102510 | Suppose that A and B are events such that P(A) = 0.75 and P(A & B) = 0.25. Determine P(B | A). |
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| m102511 | Suppose that A and B are events such that P(A) = 2/7 and P(A & B) = 3/25. Determine P(B | A). |
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| m102512 | Suppose that A and B are independent events such that P(A) = 0.3 and P(B) = 0.2. Find P(A& B). |
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| m102513 | Suppose that A and B are independent events such that P(A) = 5/8 and P(B) = 4/7. Find P(A& B). |
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| m102514 | Suppose that A and B are two events.
a. What does it mean for event B to be independent of event A?
b. If event A and event B are independent, how can their joint probability be obtained from their marginal probabilities? |
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| m102515 | Suppose that A, B, and C are independent events such that P(A) = 0.8, P(B) = 0.5, and P(C) = 0.3. Find P(A& B &C). |
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| m102516 | Suppose that a simple random paired sample is taken from two populations to compare their means. Further suppose that the distribution of the paired-difference variable has a symmetric distribution. Under what conditions would the paired t-test be preferable to the paired Wilcoxon signed-rank test? Explain your answer. |
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| m102517 | Suppose that a simple random sample is taken from a finite population in which each member is classified as either having or not having a specified attribute. Fill in the following blanks.
a. If sampling is with replacement, the probability distribution of the number of members sampled that have the specified attribute is a ________ distribution.
b. If sampling is without replacement, the probability distribution of the number of members sampled that have the specified attribute is a ________ distribution.
c. If sampling is without replacement and the sample size does not exceed ________ % of the population size, the probability distribution of the number of members sampled that have the specified attribute can be approximated by a ________distribution. |
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| m102518 | Suppose that a simple random sample of size n is taken from a finite population in which the proportion of members having a specified attribute is p. Let X be the number of members sampled that have the specified attribute.
a. If the sampling is done with replacement, identify the probability distribution of X.
b. If the sampling is done without replacement, identify the probability distribution of X.
c. Under what conditions is it acceptable to approximate the probability distribution in part (b) by the probability distribution in part (a)? Why is it acceptable? |
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| m102519 | Suppose that a variable of a population has a reverse-J-shaped distribution and that two simple random samples are taken from the population.
a. Would you expect the distributions of the two samples to have roughly the same shape? If so, what shape?
b. Would you expect some variation in shape for the distributions of the two samples? Explain your answer. |
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| m102520 | Suppose that at the beginning of Year 1 you invested $10,000 in the Stivers mutual fund and $5000 in the Trippi mutual fund. The value of each investment at the end of each subsequent year is provided in the table below. Which mutual fund performed better? |
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| m102521 | Suppose that C and D are events such that P(C) = 0.5 and P(C & D) = 0.2. Determine P(D | C). |
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| m102522 | Suppose that C and D are events such that P(C) = 4/5 and P(C & D) = 3/10. Find P(D | C). |
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| m102523 | Suppose that C and D are independent events such that P(C) = 0.7 and P(D) = 0.6. Find P(C&D). |
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| m102524 | Suppose that C and D are independent events such that P(C) = 3/4 and P(D) = 2/5. Find P(C & D). |
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| m102525 | Suppose that C, D, and E are independent events such that P(C) = 7/8, P(D) = 5/7, and P(E) = 2/3. Find P(C & D & E). |
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| m102526 | Suppose that independent simple random samples are taken from two populations to compare their means. Further suppose that the two distributions of the variable under consideration have the same shape.
a. Would the non-pooled t-test ever be the procedure of choice in these circumstances? Explain your answer.
b. Under what conditions would the pooled t-test be preferable to the Mann-Whitney test? Explain your answer. |
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| m102527 | Suppose that it has been determined that "one-fourth of drivers at fault in a car accident use a certain drug."
a. Explain in words what it means to say that being the driver at fault in a car accident is positively correlated with use of the drug.
b. Under what condition on the percentage of drivers involved in car accidents who use the drug does the statement in quotes imply that being the driver at fault in a car accident is positively correlated with use of the drug? negatively correlated with use of the drug? independent of use of the drug? Explain your answers.
c. Suppose that, in fact, being the driver at fault in a car accident is positively correlated with use of the drug. Can you deduce that a cause-and-effect relationship exists between use of the drug and being the driver at fault in a car accident? Explain your answer. |
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| m102528 | Suppose that P(Z > 1.96) = 0.025. Find P(Z ≤ 1.96). |
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| m102529 | Suppose that the variable under consideration is normally distributed on each of two populations and that the population standard deviations are equal. Further suppose that you want to perform a hypothesis test to decide whether the populations have different means, that is, whether μ1 ≠ μ2. If independent simple random samples are used, identify two hypothesis-testing procedures that you can use to carry out the hypothesis test. |
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