Questions and Answers of Model Based Testing For Embedded Systems

Compare the two groups of data in Table 5.1 using the weighted Kolmogorov–Smirnov test. Plot the shift function and its 0.95 confidence band. Compare the results with the unweighted test.
Generate 20 observations from a g-and-h distribution with g = h = 0.5. (This can be done with the R function ghdist, written for this book.) Examine a boxplot of the data.Repeat this 10 times.
For the LSAT data in Table 4.3, compute a 0.95 bootstrap-t confidence interval for mean using the R function trimcibt with plotit=T. Note that a boxplot finds no outliers.Comment on the plot created
Verify Eq. (4.5) using the decision rule about whether to reject H0 described in Section 4.4.3.
Discuss the relative merits of using the R function sint versus qmjci and hdci.
For the exponential distribution, would the sample median be expected to have a relatively high or low standard error? Compare your answer to the estimated standard error obtained with data generated
Do the skewness and kurtosis of the exponential distribution suggest that the bootstrap-t method will provide a more accurate confidence interval for µt versus the confidence interval given by Eq.
If the exponential distribution has variance µ[2] = σ2, then µ[3] = 2σ3 and µ[4] = 9σ4.Determine the skewness and kurtosis. What does this suggest about getting an accurate confidence interval
The R function rexp generates data from an exponential distribution. Use R to estimate the probability of getting at least one outlier, based on a boxplot, when sampling from this distribution.
Use the R functions qmjci, hdci, and sint to compute a 0.95 confidence interval for the median based on the LSAT data in Table 4.3. Comment on how these confidence interval compare to one another.
Compute a 0.95 confidence interval for the mean, 10% mean, and 20% mean using the lifetime data listed in the example of Section 4.6.3. Use both Eq. (4.3) and the bootstrap-t method.
Compute a 0.95 confidence interval for the mean, 10% mean, and 20% mean using the data in Table 3.1 of Chapter 3. Examine a boxplot of the data and comment on the accuracy of the confidence interval
Describe situations where the confidence interval for the mean might be too long or too short. Contrast this with confidence intervals for the 20% trimmed mean and µm.
Verify that Eq. (3.29) reduces to s 2/n if no observations are flagged as being unusually large or small by 9.
Argue that if 9 is taken to be the biweight, it approximates the optimal choice for 9 under normality when observations are not too extreme.
Set Xi = i, i = 1, . . . , 20 and compute the Harrell–Davis estimate of the median. Repeat this, but with X20 equal to 1000 and then 100,000. When X20 = 100,000, would you expect xˆ0.5 or the
Repeat the previous exercise, only this time compute the biweight midvariance, the 20%Winsorized variance, and the percentage bend midvariance. Comment on the resistance of these three measures of
Next, set X20 = 200 and compute both estimates of location. Replace X19 with 200 and again estimate the measures of location. Keep doing this until the upper half of the data is equal to 200. Comment
Use results on Winsorized expected values in Chapter 2 to show that X¯ w is a Winsorized unbiased estimate of µw. 9. Set Xi = i, i = 1, . . . , 20, and compute the 20% trimmed mean and the
Use results on Winsorized expected values in Chapter 2 to show that if the error term in Eq. (3.4) is ignored, X¯t is a Winsorized unbiased estimate of µt.
Cushny and Peebles (1904) conducted a study on the effects of optical isomers of hyoscyamine hydrobromide in producing sleep. For one of the drugs, the additional hours of sleep for 10 patients were
Comment on the strategy of applying the boxplot to the data in Exercise 2, removing any outliers, computing the sample mean for the data that remain, and then estimating the standard error of this
For the data in Exercise 1, estimate the deciles using the Harrell–Davis estimator. Do the same for the data in Table 3.2. Plot the difference between the deciles as a function of the estimated
For the data in Exercise 1, compute MADN, the biweight midvariance, and the percentage bend midvariance. Compare the results to those obtained for the data in Table 3.2. What do the results suggest
In the study by Dana (1990) on self-awareness, described in this chapter (in connection with Table 3.2), a second group of subjects yielded the observations 59 106 174 207 219 237 313 365 458 497 515
Included among the R functions written for this book is the function ghdist(n,g=0,h=0)which generates n observations from a so-called g-and-h distribution (which is described in more detail in

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