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| m102885 | What about the sample size n for confi dence intervals for the difference of proportions p1 - p2? Let us make the following assumptions: equal sample sizes n = n1 = n2 and all four quantities n1p1, n1q1, n2p2, and n2q2 are greater than 5. Those readers familiar with algebra can use the procedure outlined in Problem 28 to show that if we have preliminary estimates 1 and 2 and a given maximal margin of error E for a specifi ed con fidence level c, then the sample size n should be at least
However, if we have no preliminary estimates for 1 and 2, then the theory similar to that used in this section tells us that the sample size n should be at least
(a) In Problem 17 (Myers-Briggs personality type indicators in common for married couples), suppose we want to be 99% confi dent that our estimate 1 - 2 for the difference p1 - p2 has a maximal margin of error E = 0.04. Use the preliminary estimates 1 = 289/375 for the proportion of couples sharing two personality traits and 2 = 23/571 for the proportion having no traits in common. How large should the sample size be (assuming equal sample size-i.e., n - n1 - n2)?
(b) Suppose that in Problem 17 we have no preliminary estimates for 1 and 2 and we want to be 95% con fident that our estimate 1 - 2 for the difference p1 - p2 has a maximal margin of error E = 0.05. How large should the sample size be (assuming equal sample size-i.e., n - n1 - n2)? |
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| m102886 | What advantage does the sign test have over the Wilcoxon signed-rank test? |
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| m102887 | What are an advantage and a disadvantage of using only the sample mean to estimate the population mean? |
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| m102888 | What are counting rules? Why are they important? |
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| m102889 | What are the three rules for constructing a histogram? |
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| m102890 | What are the three steps to compute an estimation formula? |
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| m102891 | What does Chebyshev s rule say about the percentage of observations in any data set that lie within
a. 1.25 standard deviations to either side of the mean?
b. 3.5 standard deviations to either side of the mean? |
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| m102892 | What does Chebyshev s rule say about the percentage of observations in any data set that lie within
a. Four standard deviations to either side of the mean?
b. 2.5 standard deviations to either side of the mean? |
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| m102893 | What does Chebyshev s rule say about the percentage of observations in any data set that lie within
a. Six standard deviations to either side of the mean?
b. 1.5 standard deviations to either side of the mean? |
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| m102894 | What does Chebyshev s rule say about the percentage of observations that lie within one standard deviation to either side of the mean? Discuss your answer. |
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| m102895 | What does the general addition rule (Formula 4.3 on page 175) mean in the context of the probabilities in a joint probability distribution?
In Formula 4.3
If A and B are any two events, then
P(A or B) = P(A) + P(B) − P(A & B). |
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| m102896 | What does the power of a hypothesis test tell you? How is it related to the probability of making a Type II error? |
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| m102897 | What does the term one-way signify in the phrase one-way ANOVA? |
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| m102898 | What happens if we want several confi dence intervals to hold at the same time (concurrently)? Do we still have the same level of confi dence we had for each individual interval?
(a) Suppose we have two independent random variables x1 and x2 with respective population means µ1 and µ2. Let us say that we use sample data to construct two 80% con fidence intervals.
Confidence interval Confidence level
A1 < µ1 < B1.......................................0.80
A2< µ2 < B2.......................................0.80
Now, what is the probability that both intervals hold at the same time? Use methods of Section 4.2 to show that
You are combining independent events. If the confi dence is 64% that both intervals hold concurrently, explain why the risk that at least one interval does not hold (i.e., fails) must be 36%.
(b) Suppose we want both intervals to hold with 90% confi dence (i.e., only 10% risk level). How much con fidence c should each interval have to achieve this combined level of confidence? (Assume that each interval has the same con fidence level c.)
Now solve for c.
(c) If we want both intervals to hold at the 90% level of confi dence, then the individual intervals must hold at a higher level of confi dence. Write a brief but detailed explanation of how this could be of importance in a large, complex engineering design such as a rocket booster or a spacecraft. |
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| m102899 | What happens to the power of a hypothesis test if the sample size is increased without changing the significance level? Explain your answer. |
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| m102900 | What happens to the power of a hypothesis test if the significance level is decreased without changing the sample size? Explain your answer. |
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| m102901 | What information does the direction of a correlation coefficient convey? |
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| m102902 | What information is provided when you report the results of a related-samples t test? |
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| m102903 | What is a probability distribution? What makes a binomial probability distribution unique? |
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| m102904 | What is another name for the empirical rule? Why is that name appropriate? |
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