A stylist at the hair care palace gathered data on

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Quantitative Methods for Business
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Chapter 3 / Exercise 15
Quantitative Methods for Business
Anderson/Sweeney
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14. A stylist at the Hair Care Palace gathered data on the number of hair colorings givenon Saturdays and weekdays.Her results are listed below.Assume the two sampleswere taken independently:Saturdays:n1= 50x1= 14weekdays:n2= 65x2= 13a.Find the Point estimate ofP1-P2and the margin of error.b.Estimate the difference in the true proportions with a 99% confidence interval.Interpret this interval.15. IfXhas an exponential distribution with parameterλ, derive a general expression forthe (100p)th percentile of the distribution. Then specialize to obtain the median.16. Find the joint and marginal densities corresponding to the cdfF(x, y) = (1-e-αx)(1-e-βy)x0y0α >0β >0.3
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Quantitative Methods for Business
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Chapter 3 / Exercise 15
Quantitative Methods for Business
Anderson/Sweeney
Expert Verified
17. Let the joint probability function ofXandYbef(x, y) =(e-(x+y)0< x <,0< y <0otherwise.a)FindP(X >1)b)FindE(Y)c)AreXandYindependent random variables?18. In investigating which of two presentations of subject matter to use in a computer-programmed course, an experimenter randomly chose two groups of 18 students each,and assigned one group to receive presentation I and the second to receive presenta-tion II. A short quiz on the presentation was given to each group and their gradesrecorded. Do the following data indicate that the difference in the mean quiz scores(hence difference in effectiveness of presentation) exists for the two methods? Find theapproximate p-value, interpret your results and state your assumptions.(α= 0.05)¯xs2Presentation I81.723.2Presentation II77.219.819. SupposeX1, X2,· · ·, Xnbe a random sample taken from a uniform distribution on theinterval (θ, θ+ 1). Show thatT=¯X-0.5 is an unbiased estimator ofθ.20. Supposef(x, y) =25(2x+ 3y); 0x1,0y1Find (
21. A random sample of sizenis drawn from the densityf(x) =θxθ-1; 0< x <1. Findthe MLE ofθ.4

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