| Four different paints are advertised as having the same drying time. To check
ID: 3060770 • Letter: #
Question
| Four different paints are advertised as having the same drying time. To check the manufacturer's claims, five samples were tested for each of the paints. The time in minutes until the paint was dry enough for a second coat to be appl ed was recorded. The following data were obtained. Excel users: The data sat is avslable in foe named Paint. AW data sets can be fouind an the premium antine datasite. Click on the datafile logo to reference the data DATA Paint 2 Paint 3 150 142 135 133 130 153 At the = .05 level uf ignificance, test to see whether the mean dryiriu time is the sarne for each type of paint. Compute the values identified belaw (to 2 decimals, if nocessary). 5um of Squares, Treatment Sum of Squares, Frror Maan Squares, Treatment Mean Squares, Emar Calculate the value of the test staistic (to 2 decimals) The p-value is Select your snwer - T What is your condusion? Check My Work remaining)Explanation / Answer
Paint 1
Paint 2
Paint 3
Paint 4
128
144
133
150
137
133
143
142
135
142
137
135
124
146
136
140
141
130
131
153
X1
X2
X3
X4
133
139
136
144
X
138
SSA=5(133-138)^2+5(139-138)^2+5(136-138)^2+5(144-138)^2=330
SSW=(128-133)^2+……..+(153-144)^2=692
MSA=330/(4-1)=110
MSW=692/(20-4)=43.25
F=MSA/MSW=110/43.25=2.54
Fcrit=3.24
Since F<Fcrit, cannot reject the null hypothesis. Thus, we conclude that there is no difference between the mean drying time
Anova: Single Factor
SUMMARY
Groups
Count
Sum
Average
Variance
Paint 1
5
665
133
47.5
Paint 2
5
695
139
50
Paint 3
5
680
136
21
Paint 4
5
720
144
54.5
ANOVA
Source of Variation
SS
df
MS
F
P-value
F crit
Between Groups
330
3
110
2.543352601
0.092764274
3.238871517
Within Groups
692
16
43.25
Total
1022
19
SS, treatment=330
SS, Error=692
MS, treatment=110
MS, Error=43.25
F=2.54
P-value=0.09
Since F<Fcrit, cannot reject the null hypothesis. Thus, we conclude that there is no difference between the mean drying time
Paint 1
Paint 2
Paint 3
Paint 4
128
144
133
150
137
133
143
142
135
142
137
135
124
146
136
140
141
130
131
153
X1
X2
X3
X4
133
139
136
144
X
138
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