## Program Evaluation | My Assignment Tutor

In the Program Evaluation and Review Technique (PERT), we are interested in the total time to complete a project that is comprised of a large number of subprojects. For illustration, let  be three independent random times for three subprojects. If these subprojects are in series (the first one must be completed before the second starts, etc.), then we are interested in the sum  If these are in parallel (can be worked on simultaneously), then we are interested in Z = max(). In the case each of these random variables has the uniform distribution with pdf , zero elsewhere, find (a) the pdf of Y and (b) the pdf of Z.

## Statistician | My Assignment Tutor

Let be the observed values of the order statistics of a random sample of size n = 3 from a continuous type distribution. Without knowing these values, a statistician is given these values in a random order, and she wants to select the largest; but once she refuses an observation, she cannot go back. Clearly, if she selects the first one, her probability of getting the largest is 1/3. Instead, she decides to use the following algorithm: She looks at the first but refuses it and then takes the second if it is larger than the first, or else she takes the third. Show that this algorithm has probability of 1/2 of selecting the largest.

## High-temperature setting | My Assignment Tutor

Refer to Exercise 4.1.1. Using expression (4.4.10), obtain a confidence interval (with confidence close to 90%) for the median lifetime of a motor. What does the interval mean? Exercise 4.1.1 Twenty motors were put on test under a high-temperature setting. The lifetimes in hours of the motors under these conditions are given below. Also, the data are in the file lifetimemotor.rda at the site listed in the Preface. Suppose we assume that the lifetime of a motor under these conditions, X, has a Γ(1, θ) distribution. (a) Obtain a histogram of the data and overlay it with a density estimate, using the code hist(x,pr=T); lines(density(x)) where the R vector x contains the data. Based on this plot, do you think that the Γ(1, θ) model is credible? (b) Assuming a Γ(1, θ) model, obtain the maximum likelihood estimate θ 9 of θ and locate it on your histogram. Next overlay the pdf of a Γ(1, θ 9) distribution on the histogram. Use the R function to evaluate the pdf. (c) Obtain the sample median of the data, which is an estimate of the median lifetime of a motor. What parameter is it estimating (i.e., determine the median of X)? (d) Based on the mle, what is another estimate of the median of X?

## Paired design | My Assignment Tutor

On page 373 Rasmussen (1992) discussed a paired design. A baseball coach paired 20 members of his team by their speed; i.e., each member of the pair has about the same speed. Then for each pair, he randomly chose one member of the pair and told him that if could beat his best time in circling the bases he would give him an award (call this response the time of the “self” member). For the other member of the pair the coach’s instruction was an award if he could beat the time of the other member of the pair (call this response the time of the “rival” member). Each member of the pair knew who his rival was. The data are given below, but are also in the file selfrival.rda. Let μd be the true difference in times (rival minus self) for a pair. The hypotheses of interest are The data are in order by pairs, so do not mix the order. (a) Obtain comparison boxplots of the data. Comment on the comparison plots. Are there any outliers? (b) Compute the paired t-test and obtain the p-value. Are the data significant at the 5% level of significance? (c) Obtain a point estimate of μd and a 95% confidence interval for it. (d) Conclude in terms of the problem.

## Dosage | My Assignment Tutor

Verzani (2014), page 323, presented a data set concerning the effect that different dosages of the drug AZT have on patients with HIV. The responses we consider are the p24 antigen levels of HIV patients after their treatment with AZT. Of the 20 HIV patients in the study, 10 were randomly assign the dosage of 300 mg of AZT while the other 10 were assigned 600 mg. The hypotheses of interest are  (a) Obtain comparison boxplots of the data. Identify outliers by patient. Comment on the comparison plots. (b) Compute the two-sample t-test and obtain the p-value. Are the data significant at the 5% level of significance? (c) Obtain a point estimate of Δ and a 95% confidence interval for it. (d) Conclude in terms of the problem.

## Data set concerning | My Assignment Tutor

Verzani (2014), page 323, presented a data set concerning the effect that different dosages of the drug AZT have on patients with HIV. The responses we consider are the p24 antigen levels of HIV patients after their treatment with AZT. Of the 20 HIV patients in the study, 10 were randomly assign the dosage of 300 mg of AZT while the other 10 were assigned 600 mg. The hypotheses of interest are (a) Obtain comparison boxplots of the data. Identify outliers by patient. Comment on the comparison plots. (b) Compute the two-sample t-test and obtain the p-value. Are the data significant at the 5% level of significance? (c) Obtain a point estimate of Δ and a 95% confidence interval for it. (d) Conclude in terms of the problem.