Four different paints are advertised as having the same drying time. To check th

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 applied was recorded. The following data were obtained: (a) Calculate the overall sample mean (x). (b) Calculate the sum of squares due to treatments (SSTR) (c) Calculate the sum of squares due to error (SSE) (d) Calculate the mean square due to error (MSE) (e) Calculate the mean square due to treatments (MSTR) (f) Calculate the F-statistic (g) What is the critical F value (F_c) at the alpha = 0.05 level of significance using df_1 = 3 and df_2 = 16? (h) Based your answers from Parts (f)-(g) what do you conclude about whether the mean drying time is the same for each type of paint?

Explanation / Answer

(a) Overall sample mean xbar- bar = (133+139+136+144)/4 = 138

(b) sum of square dure to treatments = 5 * (138 - 133)2 + 5 * (138 - 139)2 +5 * (138 - 136)2 + 5 * (138 - 144)2

= 330

(c) sum of squares due to error (SSE) = sum of all variance * (n-1) ; where n = number of samples in any group

= (5-1) [ 6.892 + 7.072 + 4.582 +7.382] = 692

(d) Mean square due to error (MSE) = (SSE)/dFin group

here dF = 4 * (5-1) = 4 * 4 = 16

so MSE = 692/16 = 43.25

(e) MSTR = SSTR/ dF between groups

= 330/3 = 110 [ as dF between groups = 4-1 = 3]

(f) F - statistic = 110/43.25 = 2.5433

(g) F critical for df1 = 3 and df2= 16 => F critical = 3.2388

(h) Here F< F critical , so we cannot reject the null and conclude that the mean drying time is the same for each type of paint.

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