(A) One must check for both homogeneity of variances and normality when needed. (B) Both of these assumptions are needed for paired groups and independent groups t-test Both statements are true. Only the first statement (A) is true. Only the second statement (B) is true. None of the statements are true. 2
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- Give an explanation why this statement is either true or false: Portfolio contains n assets. Therefore, portfolio variance for this portfolio is the function of 2n covariances and n variances.Geographer Lalli is interested in investigating whether there is a difference in average humidity in four different types of soil. To test this hypothesis, he took 10 samples for each type of soil and measured the humidity. Lalli is slippery in statistics and he decided to perform a variance analysis to analyze the data. He had started filling out a variance analysis table but could not complete it. Fervic sum Degrees Among square sums Between groups 93,85 xx xx Within groups xx xx xx Whole 290,67 xx a) Finish filling in the fields that Lalli did not manage to fill in (marked xx)b) Carry out an appropriate hypothesis test to verify Lalla's hypothesis. What conclusion can he draw (use α = 0.05)? Show all six steps.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…We are interested in determining whether or not the variances of the sales at two music stores (A and B) are equal. A sample of 16 days of sales at store A has a sample variance of 20 while a sample of 26 days of sales from store B has a sample variance of 30. The test statistic is (A) 1.50 (B) 1.69 (C) 2.25 (D) 2.50A 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 o 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 o2 23 months (squared) is most desirable for these batteries. A random sample of 30 batteries gave a sample variance of 15.4 months (squared). Using a 0.05 level of significance, test the claim that o? = 23 against the claim that o is different from 23. (f) Find a 90% confidence interval for the population variance. (Round your answers to two decimal places.) lower limit upper limit (g) Find a 90% confidence interval for the population standard deviation. (Round your answers to two decimal places.) lower limit months upper limit…
- 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?10. STATEMENTS FIRST: THE SYMBOL FOR POPULATION MEAN IS X̄ SECOND: THE SYMBOL USED TO REPRESENT SAMPLE VARIANCE IS S 2 A. IF BOTH STATEMENTS ARE TRUEB. IF BOTH STATEMENTS ARE FALSEC. IF THE FIRST IS TRUE AND THE SECOND IS FALSED. IF THE FIRST IS FALSE AND THE SECOND IS TRUE 11. STATEMENTS FIRST: IF A DISTRIBUTION HAS TWO MODES, IT IS KNOWN AS MULTIMODAL SECOND: IF EACH DATA APPEARED ONCE ONLY, THEN THE MODE IS 0 A. IF BOTH STATEMENTS ARE TRUEB. IF BOTH STATEMENTS ARE FALSEC. IF THE FIRST IS TRUE AND THE SECOND IS FALSED. IF THE FIRST IS FALSE AND THE SECOND IS TRUE12. STATEMENTS FIRST: SPREAD IS ANOTHER TERM FOR THE MEASURE OF DISPERSION SECOND: VARIANCE IS THE MOST RELIABLE MEASURE OF DISPERSION A. IF BOTH STATEMENTS ARE TRUEB. IF BOTH STATEMENTS ARE FALSEC. IF THE FIRST IS TRUE AND THE SECOND IS FALSED. IF THE FIRST IS FALSE AND THE SECOND IS TRUE3. We want to compare initial salaries of graduates with Marketing major and graduates with Finance Major. We compare the salaries of these two groups with the same GPA. Example, salary of marketing graduate with GPA 3.5 is compare with the salary of Finance graduate with the same GPA 3.5. Assume salaries are normally distributed for both groups with unequal variances. We want to study the mean of the difference of these two groups. This is a a) t-test with equal variances b) t-test with unequal variances c) t-test for paired data.
- /Skip/1 A beverage company has two bottling plants in different parts of the world. To insure uniformity in their product, the variances of the weights of the bottles at the two plants should be equal. But Stephanie, the company's vice president of quality assurance, suspects that the variance at bottling plant A is more than the variance at bottling plant B. To test her suspicions, Stephanie samples 37 bottles from bottling plant A and 33 bottles from bottling plant B, with the following results (in ounces): Bottling Plant A: 12.4, 12.4, 13.4, 14.3, 12.7, 12.7, 13.7, 12.4, 12.8, 12.4, 12.9, 12.7, 12.8, 13.3, 13.8, 12.7, 12.4, 11.9, 12.9, 13, 13.1, 12.4, 12.7, 12.6, 12.5, 13.3, 12.2, 13.3, 12.8, 12.7, 13.2, 13.1, 11.7, 13, 12.3, 13.1, 12.4 Bottling Plant B: 12.9, 12, 13.4, 12.4, 12.4, 12.9, 12.7, 12.1, 11.4, 13.1, 14.1, 12.5, 12.7, 11.5, 12.3, 12.7, 13.7, 12.6, 13.9, 12.7, 12, 12.5, 11.7, 13.6, 11.4, 13.6, 14, 12, 11.5, 12, 11.7, 13, 11.8 Perform a hypothesis test using a 3% level of…Which of the following tests is used to test if the homogeneity of variance assumption is met? Tukey HSD 99 x 99 Factorial ANOVA Levene's test Post-hoc test8. In an educational research project it is necessary to construct a controlgroup that shares some features with the experimental group. Thereare 12 children in the experimental group, and the investigator decidesthat the control group should be the same size.The mean and the variance of the variable x in the experimental groupare 6.0 and 14.00, respectively. The investigator wishes to constructthe control group so that both groups will have the same mean andvariance.After ten children have been selected for the control group, the mean oftheir -values is 5.8 and the variance is 16.36. Two additional childrenwill be selected for the control group.What should the -values of these children be so that the experimen-tal group and the control group have equal means and variances?