Can you help me with a, b, and c. I have the answers for 1, 2, and 3 which helps with a, b, and c.
The majority of taxpayers are within the four age categories: I = < 26 − 35 >, II = < 36 − 45 >, III = < 46 − 55 > and IV = < 56 − 65 >. In order to compare the income of these four categories, find the following variables:
1. Mean income for each province (there are 10 provinces) in 2014 and 2015 for each age category; you should have 4 samples of 20 numbers - each number is the average mean income of a specific province in 2014 or 2015.
2. Total mean: ¯x (adding all of the previously received numbers and dividing it by 80) and mean for each age category: ¯xI , x¯II , x¯III , x¯IV .
3. Variance for each age category: s2I , s2II , s2III , s2IV . 3
a) Test at the 10% significance level the claim that the mean income µI of a 26-35 y.o. person is different from the mean income µII of a 36-45 y.o. person.
b) Construct the 90% confidence interval for the difference of µII −µI . Can we conclude at the 10% significance level that the income in these age groups are different?
c) Can we infer at the 10% significance level that mean income for four age categories (I, II, III, IV ) are different? Should we reject H0 at the 5% significance level? Explain. (Hint: Perform the ANOVA test of comparison of the population means assuming that all of the requirements are met. Use the calculated earlier means, variances for I, II, III, IV and the total mean ¯x.)
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