Question

# A student would like to assess whether the mean amount of money spent on books during...

A student would like to assess whether the mean amount of money spent on books during the 2016-2017 school year is equal for all students in each of the four class ranks at California University (1: Freshmen, 2: Sophomores, 3: Juniors, 4: Seniors). To conduct this study, the student took a large random sample of students at California University and recorded for each student the total amount of money spent on books during the 2016-2017 school year and the class rank. The student has provided you with the ANOVA R output, the student would like to use a 5% significance level and would like your help in making sense out of it. Question 7 Subquestions 7.a 2 point(s) Joseph, the student who conducted this study, has watched tutorials on how to run an ANOVA analysis using R. He is a bit puzzled by the ouput produced from Tukey's procedure because it is showing only pairwise comparisons where the difference in the population mean amount spent on books are not statistically significant. He is convinced that he has made a computational error when running ANOVA on R. Please review the results that Joseph has provided (both ANOVA table and Tukey's output), and write a short email explaining to him why the provided Tukey's output is correct. Make sure to use particular numerical output to justify your answer. Size Saved 7.b 1 point(s) Which of the following is an appropriate estimate of the common population variance? s subscript p squared space equals M S G space equals space 24530 space d o l l a r s squared s subscript p squared space equals M S E space equals space 11107 space d o l l a r s squared s subscript p space equals square root of M S G end root space equals space 156.6206 space d o l l a r s s subscript p space equals square root of M S E end root space equals space 105.3898 space d o l l a r s s subscript p space equals M S G space equals space 24530 space d o l l a r s s subscript p space equals M S E space equals space 11107 space d o l l a r s 7.c 1 point(s) Use the ANOVA output and the summary results provided below to construct a 98% confidence interval to estimate the population mean amount of money spent on books during the 2016-2017 school year for all Freshmen at California University (group 1). top enclose x subscript 1 space plus-or-minus t to the power of asterisk times fraction numerator s subscript p over denominator square root of n subscript 1 end root end fraction t to the power of asterisk times equals 2.341 space m u l t i p l i e r space f o r space 98 percent sign space C I space u sin g space 251 space d e g r e e s space o f space f r e e d o m space s subscript p equals 110.46187 left parenthesis 1195.209 right parenthesis plus-or-minus left parenthesis 2.341 right parenthesis open parentheses fraction numerator 110.46187 over denominator square root of 52 end fraction close parentheses rightwards arrow 1195.209 plus-or-minus 35.860 W e space e s t i m a t e comma space w i t h space 98 percent sign space c o n f i d e n c e comma space t h e space p o p u l a t i o n space m e a n space a m o u n t space o f space m o n e y space s p e n t space o n space b o o k s space d u r i n g space t h e space 2016 minus 2017 space s c h o o l space y e a r space f o r space a l l space F r e s h m e n space a t space C a l i f o r n i a space U n i v e r s i t y space t o space b e space b e t w e e n space \$ 1159.35 space a n d space \$ 1231.07. top enclose x subscript 1 space plus-or-minus t to the power of asterisk times fraction numerator s subscript p over denominator square root of n subscript 1 end root end fraction t to the power of asterisk times equals 2.341 space m u l t i p l i e r space f o r space 98 percent sign space C I space u sin g space 251 space d e g r e e s space o f space f r e e d o m space s subscript p equals square root of M S E end root equals 105.3898 left parenthesis 1195.209 right parenthesis plus-or-minus left parenthesis 2.341 right parenthesis open parentheses fraction numerator 105.3898 over denominator square root of 52 end fraction close parentheses rightwards arrow 1195.209 plus-or-minus 34.2135 W e space e s t i m a t e comma space w i t h space 98 percent sign space c o n f i d e n c e comma space t h e space p o p u l a t i o n space m e a n space a m o u n t space o f space m o n e y space s p e n t space o n space b o o k s space d u r i n g space t h e space 2016 minus 2017 space s c h o o l space y e a r space f o r space a l l space F r e s h m e n space a t space C a l i f o r n i a space U n i v e r s i t y space t o space b e space b e t w e e n space \$ 1160.99 space a n d space \$ 1229.42. top enclose x subscript 1 space plus-or-minus t to the power of asterisk times fraction numerator s subscript p over denominator square root of n subscript 1 end root end fraction t to the power of asterisk times equals 2.341 space m u l t i p l i e r space f o r space 98 percent sign space C I space u sin g space 251 space d e g r e e s space o f space f r e e d o m space s subscript p equals square root of M S G end root equals 156.62056 left parenthesis 1195.209 right parenthesis plus-or-minus left parenthesis 2.341 right parenthesis open parentheses fraction numerator 156.62056 over denominator square root of 52 end fraction close parentheses rightwards arrow 1195.209 plus-or-minus 50.8450 W e space e s t i m a t e comma space w i t h space 98 percent sign space c o n f i d e n c e comma space t h e space p o p u l a t i o n space m e a n space a m o u n t space o f space m o n e y space s p e n t space o n space b o o k s space d u r i n g space t h e space 2016 minus 2017 space s c h o o l space y e a r space f o r space a l l space F r e s h m e n space a t space C a l i f o r n i a space U n i v e r s i t y space t o space b e space b e t w e e n space \$ 1144.36 space a n d space \$ 1246.05. top enclose x subscript 1 space plus-or-minus t to the power of asterisk times fraction numerator s subscript p over denominator square root of n subscript 1 end root end fraction t to the power of asterisk times equals 2.402 space m u l t i p l i e r space f o r space 98 percent sign space C I space u sin g space 51 space d e g r e e s space o f space f r e e d o m space s subscript p equals 110.46187 left parenthesis 1195.209 right parenthesis plus-or-minus left parenthesis 2.402 right parenthesis open parentheses fraction numerator 110.46187 over denominator square root of 52 end fraction close parentheses rightwards arrow 1195.209 plus-or-minus 36.7946 W e space e s t i m a t e comma space w i t h space 98 percent sign space c o n f i d e n c e comma space t h e space p o p u l a t i o n space m e a n space a m o u n t space o f space m o n e y space s p e n t space o n space b o o k s space d u r i n g space t h e space 2016 minus 2017 space s c h o o l space y e a r space f o r space a l l space F r e s h m e n space a t space C a l i f o r n i a space U n i v e r s i t y space t o space b e space b e t w e e n space \$ 1158.41 space a n d space \$ 1232.00. top enclose x subscript 1 space plus-or-minus t to the power of asterisk times fraction numerator s subscript p over denominator square root of n subscript 1 end root end fraction t to the power of asterisk times equals 2.402 space m u l t i p l i e r space f o r space 98 percent sign space C I space u sin g space 51 space d e g r e e s space o f space f r e e d o m space s subscript p equals square root of M S E end root equals 105.3898 left parenthesis 1195.209 right parenthesis plus-or-minus left parenthesis 2.402 right parenthesis open parentheses fraction numerator 105.3898 over denominator square root of 52 end fraction close parentheses rightwards arrow 1195.209 plus-or-minus 35.1050 W e space e s t i m a t e comma space w i t h space 98 percent sign space c o n f i d e n c e comma space t h e space p o p u l a t i o n space m e a n space a m o u n t space o f space m o n e y space s p e n t space o n space b o o k s space d u r i n g space t h e space 2016 minus 2017 space s c h o o l space y e a r space f o r space a l l space F r e s h m e n space a t space C a l i f o r n i a space U n i v e r s i t y space t o space b e space b e t w e e n space \$ 1160.10 space a n d space \$ 1230.31. top enclose x subscript 1 space plus-or-minus t to the power of asterisk times fraction numerator s subscript p over denominator square root of n subscript 1 end root end fraction t to the power of asterisk times equals 2.402 space m u l t i p l i e r space f o r space 98 percent sign space C I space u sin g space 51 space d e g r e e s space o f space f r e e d o m space s subscript p equals square root of M S G end root equals 156.62056 left parenthesis 1195.209 right parenthesis plus-or-minus left parenthesis 2.402 right parenthesis open parentheses fraction numerator 156.62056 over denominator square root of 52 end fraction close parentheses rightwards arrow 1195.209 plus-or-minus 52.16699 W e space e s t i m a t e comma space w i t h space 98 percent sign space c o n f i d e n c e comma space t h e space p o p u l a t i o n space m e a n space a m o u n t space o f space m o n e y space s p e n t space o n space b o o k s space d u r i n g space t h e space 2016 minus 2017 space s c h o o l space y e a r space f o r space a l l space F r e s h m e n space a t space C a l i f o r n i a space U n i v e r s i t y space t o space b e space b e t w e e n space \$ 1143.04 space a n d space \$ 1247.38.

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