In Lecture 6, we defined the Wilcoxon rank sum test statistic W as the sum of the ranks of the Y observations in the combined sample. Now, let W' be the sum of the ranks of the X observations. Please verify the following equation: (m + n)(m + n + 1) W' + W = where m and n are number of X and Y observations, respectively.

In Lecture 6, we defined the Wilcoxon rank sum test statistic W as the sum of the ranks of the Y observations in the combined sample. Now, let W' be the sum of the ranks of the X observations. Please verify the following equation: (m + n)(m + n + 1) W' + W = where m and n are number of X and Y observations, respectively.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

For 50 randomly selected speed dates, attractiveness ratings by males of their female date partners (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings range from 1 to 10. The 50 paired ratings yield x-6.4, y= 6.1, r= - 0.226, P-value = 0.115, and y = 7.81 - 0.269x. Find the best predicted value of y (attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is x= 6. Use a 0.10 significance level. The best predicted value of y when x= 6 is (Round to one decimal place as needed.)
Suppose that the average salary of health systems professionals is normally distributed with µ=KES 40,000 and σ = KES 10,000. (20 Marks) What proportion of professionals will earn KES 24,800 or less? What proportion of professionals will earn KES 53,500 or more? What proportion of professionals will earn between KES 45,000 and KES 57,000? Calculate the 80th percentile. Calculate the 27th percentile
la). The null hypothesis is that the difference in the grams of sugar between ultra-processed and processed food μ = 0 (Ho: μ = 0). Write an example alternative hypothesis for the mean (µ) difference between ultra-processed foods (up) and processed foods (μ). 1b). Next, generate 1,000 samples. Let's say that you asked students in our class to calculate the difference in the amount of sugar between their ultra-processed food and processed food at home, which had a mean (u) sugar difference of 14.75 grams of sugar. Do you have evidence to reject the null hypothesis? 1c). Let's say that your sample difference in the amount of sugar between ultra-processed food and processed food at home was 4.75 grams of sugar. Do you have evidence to reject the null hypothesis? 1d). What is a 92% confidence interval for the data? Please write it using the full confidence interval interpretation language (e.g., I am 92% confident that...). le). What percent of the data lie to the left of -14.25 grams of…
The random variables X,Y have variance Var(X)=36 and Var(Y)=1 and their correlation is Cor(X,Y)=−3/4. Calculate Var(X+Y) with a full explanation
5. Oxygen demand is a term blologists use to describe the axygen needed by fish and other aquatic organisms for survval. The Environmental Protection Agency conducted a study of a wetland area in Marin County, Californla. In this wetland environment, the mean oxygen demand was u=9.9 mg/L, and a= 1.7 mg/L. (Reference: EPA Report 832-R- 93- 005). Let x be a random varlable that represents oxygen demand in this wetland environment. Assume x has a probability distribution that is approximately normal. a. An oxygen demand below 8 mg/L Indicates that some organisms In the wetland environment may be dying. What is the probability that the oxygen demand will fall below 8 mg/L? b. A high oxygen demand can also indicate trouble. An oxygen demand above 12 mg/L may indicate an overabundance of organisms that endanger some types of plant life. What is the probability that the oxygen demand will exceed 12 mg/L?
A weight-loss program wants to test how well their program is working. The company selects a simple random sample of 51 individual that have been using their program for 15 months. For each individual person, the company records the individual's weight when they started the program 15 months ago as an x-value. The subject's current weight is recorded as a y-value. Therefore, a data point such as (205, 190) would be for a specific person and it would indicate that the individual started the program weighing 205 pounds and currently weighs 190 pounds. In other words, they lost 15 pounds. When the company performed a regression analysis, they found a correlation coefficient of r = 0.707. This clearly shows there is strong correlation, which got the company excited. However, when they showed their data to a statistics professor, the professor pointed out that correlation was not the right tool to show that their program was effective. Correlation will NOT show whether or not there is…
Let S1^2 be the sampling variance for a random sample of twelve values (amount of mercury in the blood) and let S2^2 be the sampling variance for a random sample of ten values (amount of lead in the blood); samples from the same population were used. The population variance for mercury measurements is assumed to be twice the corresponding population variance for lead measurements. We will further assume that S1^2 is independent of S2^2. 1. Find a number b such that P [(S1^2/S2^2)<=b]=0.95 enter such a b to three decimal places b= 2. Consider the number b calculated above, find a number a such that P[a<=(S1^2/S2^2)<=b]=0.90 enter said a to three decimal places. a=
Assume that IQ scores are normally distributed with μ = 100 and σ = 15 What IQ score would be needed to score in the top 2% of IQ scores?
A random sample of n = 19 winter days in Denver gave a sample mean pollution index x1 = 43. Previous studies show that o1 = 10. For Englewood (a suburb of Denver), a random sample of n2 = 18 winter days gave a sample mean pollution index of x2 = 34. Previous studies show that o2 = 13. Assume the pollution index is normally distributed in both Englewood and Denver. Do these data indicate that the mean population pollution index of Englewood is different (either way) from that of Denver in the winter? Use a 1% level of significance. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: H1 H2 O Ho: H1 = l2; H1: H1 < µ2 (b) What sampling distribution will you use? What assumptions are you making? O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's…