A study is made of the effect of curing temperature on the compressive strength

Question

A study is made of the effect of curing temperature on the compressive strength of a certain type of concrete. Five concrete specimens are cured at each of four temperatures, and the compressive strength of each specimen is measured(in MPa). The results are as follows: Assume equal variances and alpha = 0.05. ANOVA analysis may be performed to check if the mean strength differs with temperature. Use 4DP for all your solutions H_0 and H_1 are stated as: H_0: mu_1 = mu_2 = mu_3 = mu_4 H1: mu j not all equal a. SSA = SSW = b. MSA = MSW = c. F test statistic F_stat = d. Critical value F_0, or 1 or 2 = e. Decision: we (fill in the blank by should or should not) reject the null hypothesis.

Explanation / Answer

a) SSA = Sum of Squares between Temperatures = 202.4420 SSW = Sum of Squares within Temperatures = 18.0760 b) MSA = Mean Sum of Squares between Temperatures = 67.4807 MSW = Mean Sum of Squares within Temperatures = 1.1298 c) F-statistic = MSA/MSW           = 67.4806/1.1298 = 59.7306 F-statistic = 59.7306 d) Critical Value F, df1, df2 = F0.05, 3, 16 df1 = number of temperature groups - 1 = 4 - 1 = 3 df2 = total observations - number of temperature groups = 20 - 4 = 16 Critical Value F0.05, 3, 16   =   3.2389 e) Since F-statistic (59.7306) > F-critical (3.2389), we should reject the null hypothesis that is the j are not equal

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