Question

(23 pts) You have two populations of consumer (male/female) and three different kinds of hair gel (P&G/U/TK). You want to evaluate their effectiveness on your two populations by recording the number of hours the gel worked on each individual. P&GTUTIK Male 10.7 11.5 125 11.1 14.1 123 9.6 6.8 1 ANOVA INOV 10.6 10.7 8.7 6.7 10.0 9.3 9.7 T 10.3 110 11.0 109 | 9.7 7.7 13.1 T 14.5 8.7 61 8.6 female 9.9 9.0 8.6 0.9 9.6 10.1 12.2 10.6 5.0 11.6 12.5 6.3 10.7 13.6 921 1.3 39 2.6 10.7 6.9 13.5 3.4 5.3 9.3 10.1 13.4

please solve it in detail. thank you!

Answer 1

This is a 2-way ANOVA problem which I have solved in MINITAB 2017

ANOVA: P&G, U, TK versus Gender

Factor Type Levels Values
Gender random 2 F, M

Analysis of Variance for P&G

Source DF SS MS F P
Gender 1 14.240 14.240 1.67 0.210
Error   20 170.138 8.507
Total    21 184.379

S = 2.91666 R-Sq = 7.72% R-Sq(adj) = 3.11%

Here the treatment effects are not statistically significant at 5% level of significance as the p-value is more than 0.05

Analysis of Variance for U

Source DF SS MS F P
Gender 1 0.691 0.691 0.09 0.772
Error 20 160.824 8.041
Total 21 161.515

S = 2.83570 R-Sq = 0.43% R-Sq(adj) = 0.00%

Here the treatment effects are not statistically significant at 5% level of significance as the p-value is more than 0.05

Analysis of Variance for TK

Source DF SS MS F P
Gender 1 47.13 47.13 4.38 0.049
Error    20 215.18 10.76
Total 21 262.31

S = 3.28011 R-Sq = 17.97% R-Sq(adj) = 13.87%

Here the treatment effects are statistically significant at 5% level of significance as the p-value is less than 0.05