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A biologist considered studying the effects of various environmental pollutants on the health of mice by using a 27- 4 fractional factorial design.
a. How many factors are involved? How many levels are there for each factor? How many trials will be required for a single replicate of the experiment? Can a test for lack of fit be obtained?
b. The biologist decided to augment the design with six center-point replicates. Can a test for lack of fit now be obtained? If so, can the biologist determine which factors caused a curvature effect?
Based on the custom "rule-of-thumb" for estimating the standard deviation, if the range of prices for a product sold in Kansas City is between $99 and $349, an estimate of the standard deviation of the prices would be about:
Merta reports that 74% of its trains are on time. A check of 60 randomly selected trains shows that 38 of them arrived on time. Find the probability that among the 60 trains 38 or fewer arrive on time.
Can we conclude that the mean age of the population from which the sample may be presumed to have been drawn is less than 60 years? Let α = .05
What values would be appropriate for the performance measures listed in the preceding problem for the case in which two tellers are available?
Find E(L), Var(L), Var(1L). Find the probability that, for a given contract, the premiums collected will be sufficient to pay the benefits.
When the rats In the sample reach 10 weeks old, each rat is weighed. The mean weight for this sample is M=974. Sketch the appropriate distribution, and locate the critical region for the alpha level =.05.
Compute a value V that enables us to state, with 90 percent confidence, that population variance (sigma^2) is less than V.
Let x denote the distance from the lower left-hand corner A of the square to the selected point. What are possible values of x? Is x a discrete or a continuous variable?
A person asks, "what do you think is the ideal number of children for a family to have?" The 497 females who responded had a median of 2, mean of 3.02, and a standard deviation of 1.81.
A receiver in the ship's control room receives R = V +X, The random variable X is a Gaussian (0, √3) noise voltage that is independent of V. The receiver uses R to calculate a linear estimate of the telemetry voltage:
Consider the linear transformation T : complex numbers^n -> complex numbers^n given by T( z1, z2, ... , zn ) = ( a1z1, a2z2, ... , anzn). What is the dimension of the subspace spanned by the eigenvectors of T? Exhibit a basis for this space, and g..
Girls' cross-country times: a contrast (optional). Continue your analysis of the data from the previous problem by comparing average race time during the first half of the season with the average for the second half.
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