Question

In: Statistics and Probability

Four different paints are advertised to have the same drying times.  To verify the manufacturer’s claim, seven...

  1. Four different paints are advertised to have the same drying times.  To verify the manufacturer’s claim, seven samples were tested for each of the paints.  The time in minutes until the paint was dry enough for a second coat to be applied was recorded.  Below are the results which may be imported into MSExcel for analysis:  (Assume the populations are normally distributed, the populations are independent and the population variances are equal)

Paint 1

Paint 2

Paint 3

Paint 4

120

120

117

128

112

130

122

131

121

121

123

131

118

126

115

129

118

126

123

127

121

114

126

126

118

117

126

137

  1. Write the Null and Alternative hypothesis to test whether there is a difference in dry time between the samples of each paint?
  1. What statistic would you use to analyze this?

  1. At a 0.01 level of significance, what would be your decision rule?
  1. From your analysis, is there a difference between drying times?

  1. If there was a difference in dry times how would you determine which paint has the different drying time? (i.e.  what formula would you use and what is your decision criteria?) (this is not asking for a calculation)

please show all the work

Solutions

Expert Solution

A)

Ho: µ1=µ2=µ3=µ4
H1: not all means are equal

.....

B)

F stat will be used

treatment G1 G2 G3 G4
count, ni = 7 7 7 7
mean , x̅ i = 118.286 122.00 121.71 129.86
std. dev., si = 3.1 5.6 4.2 3.7
sample variances, si^2 = 9.571 31.667 17.905 13.476
total sum 828 854 852 909 3443 (grand sum)
grand mean , x̅̅ = Σni*x̅i/Σni =   122.96
( x̅ - x̅̅ )² 21.889 0.930 1.563 47.511
TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² = 153.223 6.509 10.938 332.580 503.25
SS(within ) = SSW = Σ(n-1)s² = 57.429 190.000 107.429 80.857 435.7143

no. of treatment , k =   4  
df between = k-1 =    3  
N = Σn =   28  
df within = N-k =   24  
      
mean square between groups , MSB = SSB/k-1 =    503.25/3=   167.7500
mean square within groups , MSW = SSW/N-k =    435.7143/24=   18.1548
      
F-stat = MSB/MSW =    167.75/18.1548=   9.24
      
P value =   0.0003  

anova table
SS df MS F p-value
Between: 503.3 3 167.8 9.24 0.000
Within: 435.7 24 18.2
Total: 939.0 27

F =9.24

................

c)

α =    0.01

F-critical = 4.718

so, f stat should be greater than 4.718

d)



Decision:  f stat > critical , reject null hypothesis

so, there is difference between drying times

....

e)

tukey kramer rule:

critical value = q*√(MSE/2*(1/ni+1/nj))

if absolute difference of means > critical value,means are significnantly different ,otherwise not

........................

Please let me know in case of any doubt.

Thanks in advance!


Please upvote!


Related Solutions

Four different paints are advertised to have the same drying times. To verify the manufacturer’s claim,...
Four different paints are advertised to have the same drying times. To verify the manufacturer’s claim, seven samples were tested for each of the paints. The time in minutes until the paint was dry enough for a second coat to be applied was recorded. Below are the results which may be imported into MSExcel for analysis: (Assume the populations are normally distributed, the populations are independent and the population variances are equal) Paint 1 Paint 2 Paint 3 Paint 4...
Four different paints are advertised to have the same drying times. To verify the manufacturer’s claim,...
Four different paints are advertised to have the same drying times. To verify the manufacturer’s claim, seven samples were tested for each of the paints. The time in minutes until the paint was dry enough for a second coat to be applied was recorded. Below are the results which may be imported into MSExcel for analysis: (Assume the populations are normally distributed, the populations are independent and the population variances are equal) Paint 1 Paint 2 Paint 3 Paint 4...
5. Four different paints are advertised to have the same drying times. To verify the manufacturer’s...
5. Four different paints are advertised to have the same drying times. To verify the manufacturer’s claim, seven samples were tested for each of the paints. The time in minutes until the paint was dry enough for a second coat to be applied was recorded. Below are the results which may be imported into MSExcel for analysis: (Assume the populations are normally distributed, the populations are independent and the population variances are equal) Paint 1 Paint 2 Paint 3 Paint...
Four different paints are advertised to have the same drying times. Use the Kruskal Wallis Test...
Four different paints are advertised to have the same drying times. Use the Kruskal Wallis Test – Analysis of Variance by Ranks, to verify the manufacturer’s claim. Remember that seven samples were tested for each of the paints. The time in minutes until the paint was dry enough for a second coat to be applied was recorded. Below are the results.    Paint 1 Rank Paint 2 Rank Paint 3 Rank Paint 4 Rank 114 112 126 115 117 118...
Chapter 16 Four different paints are advertised to have the same drying times.  Use the Kruskal Wallis...
Chapter 16 Four different paints are advertised to have the same drying times.  Use the Kruskal Wallis Test – Analysis of Variance by Ranks, to verify the manufacturer’s claim.  Remember that seven samples were tested for each of the paints.  The time in minutes until the paint was dry enough for a second coat to be applied was recorded.  Below are the results.     Paint 1 Rank Paint 2 Rank Paint 3 Rank Paint 4 Rank 114 112 126 115 117 118 127 117 120...
Four different paints are advertised as having the same drying time. To check the manufacturer's claims,...
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 applied was recorded. The following data were obtained. We wish to test at 5% significance whether mean drying time is same for each type of paint. Treated Sum of Squares = 330 and Error Sum of Squares = 692....
In a study to compare the visibility of paints used on highways, four different types of...
In a study to compare the visibility of paints used on highways, four different types of paint were tested at three different locations. It is to be expected that paint wear will differ depending on the quantity and type of traffic on the road, so Highway was used as a blocking factor. The following table gives the amount of visibility of paint after a set period of exposure to traffic and weather; visibility was measured on a standard scale, with...
A paint manufacturer wishes to compare the drying times of two different types of paint. Independent...
A paint manufacturer wishes to compare the drying times of two different types of paint. Independent random samples of 11 cans of Type A and 9 cans of Type B were selected and applied to a similar surface. The drying times were recorded. Type A had a mean drying time of 68.9 with a standard deviation of 0.5. Type B had a mean drying time of 70.6 with a standard deviation of 3. Do the data provide sufficient evidence at...
A paint manufacturer wished to compare the drying times of two different types of paint. Independent...
A paint manufacturer wished to compare the drying times of two different types of paint. Independent simple random samples of 11 cans of type A and 9 cans of type B were selected and applied to similar surfaces. The drying times, in hours, were recorded. The summary statistics are as follows. Type A Type B 1 = 76.9 2= 63.7 s1 = 4.5 s2 = 5.1 n1 = 11 n2 = 9 Construct a 98% confidence interval for   the difference...
Two competing household paint companies claim to have quick-drying paint. An experiment was performed to compare...
Two competing household paint companies claim to have quick-drying paint. An experiment was performed to compare the mean lengths of time required for the paints to dry for brand A and brand B. Twelve randomly selected 10 x 10 squares of drywall were painted with brand A. Another 12 were randomly selected and painted with brand B. The lengths of time in minutes for the paint to dry were recorded. The means, standard deviations, and sizes of the two samples...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT