Consider a 6 x 2 data matrix 19 12 22 6 69 3 15 2 13 20 5 of 6 observations of 2 variables. (a) Find the sample covariance matrix of the data. (b) Find the component of the data corresponding to the largest variance.
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- Captopril is a drug designed to lower systolic blood pressure. In a trial, 12 randomly selected subjects were treated with the drug and another 12 randomly selected subjects were treated with the placebo. Assume the two populations are normally distributed. The results and some summary statistics are shown in the table. Note that some of the summary statistics may not be useful or relevant! Data Group Placebo 200 174 198 170 179 182 193 209 185 155 169 210 (ž1 = 185.3) (s1 = 17.1) Captopril (I2 = 166.8) (s2 = 14.9) d = I1 – 12 (d = 18.6) (sa = 10.1) %3D %3D 191 170 177 167 159 151 176 183 159 145 146 177 9. 4 21 3 20 31 17 26 26 10 23 33 %3D data %3D Using a 0.01 significance level, is there sufficient evidence to support the claim that the mean systolic blood pressure is lower for those treated with the drug than for those treated with the placebo? Use the p-value method. For full marks, include a diagram of the distribution indicating important components of the question.Two computer companies are offering new software to universities. Let X and Y denote the number of software installed in three major universities by these two companies. Suppose that the variance of X is 539, the variance of Yis 754, and the covariance of X and Yis 183.50. a) Calculate the correlation coefficient (p) Select one: a. 0.287 b. 0.857 c. None of the answers d. 0.928Suppose that the correlation coefficient ρ between two random variables has been found in an experiment to be zero. Which of the following is NOT TRUE?
- 4One professor who teaches statistics gave students one homework assignment. He asked students to find a two-variable data set and compute the Pearson correlation coefficient. One student found a data set: one variable is students' midterm test score in an introductory microeconomics class and total observations are 45 students; while the other one variable is also students' midterm test score in another introductory microeconomics class and total observations are 57 students. Both of these two classes were taught by the same instructor in spring 2018. Does this student's data set make sense? Why or why not? Discuss and explain your reasons. You must provide your statistical analysis and reasons.A set of solar batteries is used in a research satellite. The satellite can run on only one battery, but it runs best if more than one battery is used. The variance σ2 of lifetimes of these batteries affects the useful lifetime of the satellite before it goes dead. If the variance is too small, all the batteries will tend to die at once. Why? If the variance is too large, the batteries are simply not dependable. Why? Engineers have determined that a variance of σ2 = 23 months (squared) is most desirable for these batteries. A random sample of 22 batteries gave a sample variance of 13.2 months (squared). Using a 0.05 level of significance, test the claim that σ2 = 23 against the claim that σ2 is different from 23. (a) What is the level of significance? Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) What are the degrees of freedom? (f) Find a 90% confidence interval for the population variance. (Round your answers to two decimal…
- A set of solar batteries is used in a research satellite. The satellite can run on only one battery, but it runs best if more than one battery is used. The variance σ2 of lifetimes of these batteries affects the useful lifetime of the satellite before it goes dead. If the variance is too small, all the batteries will tend to die at once. Why? If the variance is too large, the batteries are simply not dependable. Why? Engineers have determined that a variance of σ2 = 23 months (squared) is most desirable for these batteries. A random sample of 20 batteries gave a sample variance of 13.8 months (squared). Using a 0.05 level of significance, test the claim that σ2 = 23 against the claim that σ2 is different from 23. (a) What is the level of significance?State the null and alternate hypotheses. A. Ho: σ2 = 23; H1: σ2 ≠ 23 B. Ho: σ2 = 23; H1: σ2 < 23 C. Ho: σ2 = 23; H1: σ2 > 23 D. Ho: σ2 > 23; H1: σ2 = 23 (b) Find the value of the chi-square statistic for the sample. (Round…A manufacturing company is interested in buying one of two different kinds of machines for production purposes. The first machine was run for 20 hours. It produces on average of 40 items per hour with variance of 8 items2. The second machine was run for 15 hours. It produces on average 50 items per hour with variance of 10 items2. Assume that the production per hour for each machine is (approximately) normally distributed and there a homogeneity between the populations' variances of the number of items produced by the 2 machines Compute 90% confidence interval for the difference between the two means. What is the tabulated value What is the S.E value What Is the lower and upper boundMindForce also collected the data regarding errors/nonconformities in orders placed due to system errors and the data for 10 samples is given below. Sample No. 1 2 3 4 5 6 7 8 9 10 Sample Size 200 200 200 200 200 200 200 200 200 200 Nonconformities 3 2 6 4 11 20 5 7 2 0 Implement p-chart for errors in orders placed at MindForce and analyze the variability.
- It is hypothesized that the total sales of a corporation should vary more in an industry with active price competition than in one with duopoly and tacit collusion. In a study of the merchant ship production industry it was found that in 4 years of active price competition, the variance of company A’s total sales was 114.09. In the following 7 years, during which there was duopoly and tacit collusion, this variance was 16.08. Assume that the data can be regarded as an independent random sample from two normal distributions. 1. Test, at the 5% level, the null hypothesis that the two population variances are equal against the alternative that they are not equal.8 If the analysis of variance F-test leads to the conclusion that at least one of the model parameters is nonzero, can you conclude that the model is the best predictor for the dependent variable y? Can you conclude that all of the terms in the model are important for predicting y? What is the appropriate conclusion?I've created a Correlation Matrix in Microsoft Excel. I need to identify 4 pairs of variables that have the highest correlation. How would I do this? The matrix is attached to this question.