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2. -/16.66 points You may need to use the appropriate technology to answer this question To study the effect of temperature on yield in a chemical process, five batches were produced at each of three temperature + ASWSBE 131 3.Е.009.MI My Notes Ask Your Teacher levels. The results follow Temperature 50°C 60°C 70°C 31 30 35 23 26 35 23 37 24 27 29 29 36 25 Construct an analysis of variance table. (Round your values for MSE and F to two decimal places, and your p-value to four decimal places.) Source of Variation Sum Degrees of Freedom Mean of Squares Square p-value Treatments Error Total

Use a 0.05 level of significance to test whether the temperature level has an effect on the mean yield of the process State the null and alternative hypotheses a: μ50°C- 1160°C- 1170°C H Not all the population means are equal HO: At least two of the population means are equal Ha: At least two of the population means are different. Ho: Not all the population means are equal Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion Do not reject Ho. There is not sufficient evidence to conclude that the mean yields for the three temperatures are not equal Reject H0. There is sufficient evidence to conclude that the mean yields for the three temperatures are not equal O Do not reject Ho. There is sufficient evidence to conclude that the mean yields for the three temperatures are not equal Reject H0. There is not sufficient evidence to conclude that the mean yields for the three temperatures are not equal

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>y-c (2, 4,6,5,7,8,6, 5, 9,8, 23, 34, 43, 32, 22) > x-c (rep (c (A, в, C) , 5) ) >x-factor (x) > X [1] A B CABCA BCABCA B C Levels: A B C yc (35, 31,24,23,30,27,37,35, 29,40,23,28,25,26,36) xc (rep (c (A, B, C), 5)) > x-factor (x) fit-aov (y~x) summary(fit) Df Sum Sq Mean Sq F value Pr (>F) 2 32.1 16.070.491 0.624 Residuals 12 392.8 32.73Here the table of ANOVA is given above. here we use R software.

We assume H0=mu(50C)=mu(60C)=mu(70C)

H1=Not all the populations means are equal.

* The value of the test statistic is 0.491 i.e Fcal value.

* The corresponding p value = 0.624

* Since here p value is very good to accept H0, therefore

Do not reject H0. There is not sufficient evidence to conclude that the mean yields for the three temperatures are not equal.

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