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Suppose we wish to test. H0: the X and Y distributions are identical versus Ha: the X distribution is less spread out than the Y distribution The accompanying figure pictures X and Y distributions for which Ha is true. The Wilcoxon rank-sum test is not appropriate in this situation because when Ha is true as pictured, the Y's will tend to be at the extreme ends of the combined sample (resulting in small and large Y ranks), so the sum of X ranks will result in a W value that is neither large nor small.
Consider modifying the procedure for assigning ranks as follows: After the combined sample of m + n observations is ordered, the smallest observation is given rank 1, the largest observation is given rank 2, the second smallest is given rank 3, the second largest is given rank 4, and so on. Then if Ha is true as pictured, the X values will tend to be in the middle of the sample and thus receive large ranks. Let W' denote the sum of the X ranks and consider an uppertailed test based on this test statistic. When H0 is true, every possible set of X ranks has the same probability, so 'the same distribution as does W when H0 is true. The accompanying data refers to medial muscle thickness for arterioles from the lungs of children who died from sudden infant death syndrome (x's) and a control group of children (y's). Carry out the test of H0 versus Ha at level .05.
Consult the Lehmann book (in the chapter bibliography) for more information on this test, called the Siegel-Tukey test.
Does the effect of education vary by gender? Construct any interaction variables you need and test the joint hypothesis using appropriate restricted and unrestricted regressions.
Why does Maria Perez want to conduct business transactions using cash (not check or credit card)? How should Jas respond to Maria's suggestion?
a motor bike battery manufacturer found that the life of their batteries is normally distributed with a mean life span
The test must be performed at the 5% level of significance. According to the null hypothesis, the value of the population mean is parts per million.
For each player, determine the minimum, the first quartile, the median, the third quartile, and the maximum of their home run totals. Use these results to construct comparative box-and-whisker plots.
Would the method described above be a good way to determine which team was taller (explain why or why not)?
A quality control engineer selects a part to be tested. The part is then declared acceptable, repairable, or scrapped. Then another part is tested. List all the possible outcomed of this experiment.
A test statistic is computed from sample data in hypothesis testing and is used in making a decision about whether or not to reject the null hypothesis. True or False
Replacement times for new Ford Taurus GL automobiles are normally distributed with a mean of 7.1 years and a standard deviation of 1.4 years.
Four couples, each consisting of one man and one woman, are seated at a circular table. Assuming that each different order is equally likely, find the probability that:
Assuming that Mendel's proportion of 3/4 is correct, find the probability of getting 787 or fewer plants with long stems among 1064 offspring plants. compare answers with binomial and normal approximation.
in sundays indianapolis star there was an artcle talking about all the new grocery stroes opening in indy. one of the
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