(Solved): please answer Fully Assignment: (50 points) - Chapter 10, pg. 370, problem 10.76 One-Way ANOVA The A ...

Assignment: (50 points) - Chapter 10, pg. 370, problem 10.76 One-Way ANOVA The American Society for Quality (ASQ) conducted a salary survey of all its members. ASQ members work in all areas of manufacturing and service-related institutions, with a common theme of an interest in quality. Two job titles are a black belt and green belt. (See Section 14.6 for a description of these titles in a Six Sigma quality improvement initiative.) Descriptive statistics concerning salaries for these two jobs titles are given in the following table: Job Title Sample Size Mean Standard Deviation Black Belt 128 93,123 21.186 Green Belt 39 73,045 21.272 Source: Data extracted from "Op Salary Survey." Chuality Press, December 2013, p. 17 a) (20 points) Using a 0.05 level of significance, is there a difference in the variability of salaries between black belts and green belts? Hint 1: Figure out the formula for Sample variance for each sample (orange fields. Once you add the formulas, the rest of the fields will calculate automatically. Consider questions: Which test do we use for the ratio of two variances? If the standard deviation (6) is given, how do you calculate variance? Hint 2: To make a decision, we will use this rule: If p-value 0.05, reject H, Answer if we should reject our hypothesis H. or not (based on your calculations.) Indicate if there is enough evidence in the variability of salaries between Black Belts and Green Belts. b) (20 points) Based on the result of (a), which t-test defined in Section 10.1 is appropriate for comparing mean salaries? Hint: Read Section 10.1 and determine which t-test should be used based. c) (10 points) Using a 0.05 level of significance, is the mean salary of black belts greater than the mean salary of green belts? Hint 1: Figure out the formula for degree of freedom for both samples and the total degree of freedom (orange fields.) Once you add the formulas, the rest of the fields will calculate automatically. Please review how to calculate the degree of freedom given the sample size and total degree of freedom. Hint 2: To make a decision, we will use the same rule as (a): If p-value < 0.05, reject H, Answer if we should reject our hypothesis H, or not (based on your calculations.) Indicate if there is enough evidence that the mean salary of Green Belts is less than the mean salary of Black Belts.