STATISTICS

ANOVA, ANCOVA, REGRESSION

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 pictures.

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 Which of the following table is true? a. Laboratory Mean Standard deviation A 59.66 1.4082 B 61.96 2.1606 C 56.52 1.1628 D 61.12 0.7694 Laboratory Mean Standard deviation A 59.68 1.4081 B 61.94 2.1606 C 56.52 1.1628 D 61.14 0.7693 Laboratory Mean Standard deviation A 59.66 1.4082 B 61.95 2.1601 C 56.52 1.1629 D 61.12 0.7695 d Laboratory Mean Standard deviation A 59.65 1.4085 B 61.96 2.1606 C 56.51 1.1625 D 61.12 0.7694Suppose that an experiment on cognitive behavioral modification for children, especially their reaction (in seconds) to the question, "Who wants to be a people helper when you are a grownup?" is planned. Listed in Table I are the reaction times for 3 third graders from three separate schools. Perform an ANOVA at 0.05 level of significance. Table 1. Reaction Time (seconds) School 1 School 2 School 3 5 4 8 10 7 9 15 12 17 2 5 10 18 The value of SSC, and SSE are a. 1.7 and 393.3, respectively b. 1.9 and 396.3, respectively c. 1.5 and 393.1, respectively d. 1.6 and 392.3, respectivelySix 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 4 5 6 17.5 16.4 20.3 14.6 17.5 18.3 16.9 19.2 15.7 16.7 19.2 16.2 15.8 17.7 17.8 20.8 16.5 17.5 18.6 15.4 18.9 18.9 20.5 20.1 After the ANOVA was performed, is it necessary to carry out a DMRT? a. No, the null hypothesis is rejected. b. Yes, because the null hypothesis is accepted. c. Yes, the null hypothesis is rejected. d. No. because the null hypothesis is accepted.Suppose that an experiment on cognitive behavioral modification for children, especially their reaction (in seconds) to the question, "Who wants to a people helper when you are a grownup?" is planned. Listed in Table I are the reaction times for 3 third graders from three separate schools. Perform an ANOVA at 0.05 level of significance. Table 1. Reaction Time (seconds) School1 School 2 School 3 5 4 8 10 2 7 9 15 12 17 2 5 10 18 The computed value of fis a. 0.027 b. 0.021 c. 0.025 d. 0.028A Q-Q plot (or quantile-quantile plot) draws the correlation between a given sample and the normal distribution. It is used to check visually if the given the data follows the normal distribution. Suppose a Q-Q plot is given below: 40 sample 20 theoretical What is the correct interpretation of the Q-Q plot? I. As all the points fall approximately along this reference line, we cannot assume normality. II. As all the points fall approximately along this reference line, we can assume normality. III. As some of the points fall approximately along this reference line, we cannot assume normality. IV. As some of the points fall approximately along this reference line, we can assume normality. a. I only b. II only c. III only d. IV only