Question

3. The tensile strength of Portland cement is being studied. Four different mixing techniques can be used economically. A completely randomized experiment was conducted and the following data were collected Mixing Technique Tensile Strength (lb/in2) 3129 3200 2800 2600 3000 2865 3300 2975 2900 2985 2700 2600 2890 3150 3050 2765 (a) Test the hypothesis that mixing techniques affect the strength of the cement. State the model, hypotheses, test statistic, decision rule, ANOVA table and decision clearly.

Answer 1

Answer Date: 28/02/2019 To test the hypothesis is that at least one of the mean tensile strength of the cement different among four maximum mixing techniques at 5% level ofsignificance The null and alternative hypothesis is, Ha: at least one μ, is unequal. The F-test statistics is, By using Excel software, find F-test statistics with the help of following steps 1) Import the data. 2) Choose ANOVA: Single Factor from Data Analysis in Data menu. 3) Choose Input Range and Colunn in Groups by. 4) Choose Output Range 5) Click Ok

ANOVA Source of Variation Between Groups Within Groups Total MS P-value F crit 489740.1875 153908.25 643648.4375 3 163246.7 12.72811 0.000489 3.490295 12 12825.69 15 From the Excel output, the F-test statistics is 12.73 The F-critical value for this test is. From the Excel output, the F-critical value for this test is 3.490 Decision The F-test statistics is 12.73 is greater than F-critical value which is 3.49, the null hypothesis is rejected at 5% level of significance. There is sufficient evidence that at least one of the mean tensile strength of the cement different among four maximum mixing techniques. The resultis statistically signiticant.