STATISTICS

ANOVA, ANCOVA, REGRESSION, RSTUDIO

Directions: Answer the following questions inside the picture and choose the correct answer. Explain why it is the correct answer. All the details for the question is indicated in the picture for each number.

1.

Four laboratories are being used to perform chemical analysis. Samples of the same material are sent to the laboratories for analysis as part of the study to determine whether or not they give, on the average, the same results. The analytical results for the 4 laboratories are as follows: Laboratory A B C D 58.7 62.7 55.9 60.7 61.4 64.5 56.1 60.3 60.9 63.1 57.3 60.9 59.1 59.2 55.2 61.4 58.2 60.3 58. 1 62.3 Perform the ANOVA at the 0.05 level of significance and give conclusions concerning the laboratories. The conclusion is a. There is no significant relationship among the average number of chemicals produced by the four laboratories, b. The average number of chemicals produced by the four laboratories are the same. c. There is a significant relationship among the average number of chemicals produced by the four laboratories. d. At least two of average number of chemicals produced by the four laboratories are significantly.Two data samples are independent if they come from distinct populations and the samples do not affect each other. Using the Mann-Whitney-Wilcoxon Test, we can decide whether the population distributions are identical without assuming them to follow the normal distribution. Using R. data column in the built-in dataset micars, named am, indicates the transmission type of the automobile model (0 - automatic, 1 = manual). In other words, it is the differentiating factor of the transmission type. Without assuming the data to have normal distribution, decide at 05 significance level if the gas mileage data of manual and automatic transmissions in mtcars have identical data distribution. R code and its output > wilcox. test (mpg ~ am, data=mtcars) Wilcoxon rank sum test with continuity correction data : mpg by am W = 42, p-value = 0.001871 alternative hypothesis: true location shift is not equal to 0 Warning message: In wilcox. test. default (x = c(21.4, 18.7, 18.1, 14.3, 24.4, 22.8, : cannot compute exact p-value with ties What is the correct interpretation of the data analysis using R? a. At .05 significance level, we conclude that the gas mileage data of manual and automatic transmissions in mtear are identical populations. b. At .05 significance level, we conclude that the gas mileage data of manual and automatic transmissions in micar are not significant different. c. At .05 significance level, we conclude that the gas mileage data of manual and automatic transmissions in mtear are nonidentical populations. d. At .05 significance level, we conclude that the gas mileage data of manual and automatic transmissions in mtcar are significantly different.Six different machines are being considered for use in manufacturing rubber seals. The machines are being compared with respect to tensile strength of the product. A random sample of 4 seals from each machine is used to determine whether or not the mean tensile strength varies from machine to machine. The following are the tensile strength measurements in kilograms per square centimeter x 10 7. Machine 2 3 5 17.5 16.4 20.3 14.6 17.5 18.3 16.9 19.2 15.7 167 19.2 16.2 158 17.7 17.8 20.8 165 17.5 154 18.9 20 5 20,1 After the ANOVA was performed, is it necessary to carry out a DMRI? a. No, the null hypothesis is rejected. b. Yes, because the mall hypothesis is accepted. C. Yes, the null hypothesis is rejected. d. No, because the null hypothesis is accepted