Question 9.8: Use the preceding ANOVA table to determine whether the addit......

ISE Principles of Statistics for Engineers and Scientists [987713]

Use the preceding ANOVA table to determine whether the additive model is plausible for the yield data. If the additive model is plausible, can we conclude that either the catalyst or the reagent affects the yield?

Two-way ANOVA: Yield versus Catalyst, Reagent

Source DF SS MS F P
Catalyst 3 877.56 292.521 9.36 0.000
Reagent 2 327.14 163.570 5.23 0.010
Interaction 6 156.98 26.164 0.84 0.550
Error 36 1125.33 31.259
Total 47 2487.02

S = 5.591 R-sq = 54.75% R-Sq(adj) = 40.93%

Step-by-Step

The 'Blue Check Mark' means that this solution was answered by an expert.
Learn more on how do we answer questions.

We first check to see if the additive model is plausible. The P-value for the interactions is 0.55, which is not small. We therefore do not reject the null hypothesis that all the interactions are equal to 0, and we conclude that the additive model is plausible. Since the additive model is plausible, we now ask whether the row or column factors affect the outcome. We see from the table that the P-value for the row effects (Catalyst) is approximately 0, so we conclude that the catalyst does affect the yield. Similarly, the P-value for the column effects (Reagent) is small (0.010), so we conclude that the reagent affects the yield as well.

Related Answered Questions

Question: 9.3

For the data in Table 9.1, compute MSTr, MSE, and F. Find the P-value for testing the null hypothesis that all the means are equal. What do you conclude? ...

Verified Answer:

From Example 9.2, SSTr = 743.4 and SSE = 1023.6. W...

Question: 9.6

The following output (from MINITAB) presents the ANOVA table for the weld data in Table 9.1 (in Section 9.1). Which pairs of fluxes, if any, can be concluded, at the 5% level, to differ in their effect on hardness? ...

Verified Answer:

There are I = 4 levels, with J = 5 observations at...

Question: 9.7

In Example 9.4 (in Section 9.1), several measurements of the maximum hourly con-centrations (in 𝜇g/m³) of SO2 were presented for each of four power plants, and it was concluded that the mean concentrations at the four plants were not all the same. The following output (from MINITAB) presents the ...

Verified Answer:

Among the simultaneous confidence intervals, there...

Question: 9.16

A 2^5 factorial experiment was conducted to estimate the effects of five factors on the quality of lightbulbs manufactured by a certain process. The factors were A: plant (1 or 2), B: machine type (low or high speed), C: shift (day or evening), D: lead wire mate-rial (standard or new), and E: ...

Verified Answer:

We compute the effects, using the rules for adding...

Question: 9.5

In Example 9.4, assume that it is reasonable to treat the four power plants as a random sample from a large population of power plants, and furthermore, assume that the SO2 concentrations in the population of plants are normally distributed. Can we conclude that there are differences in SO2 ...

Verified Answer:

This is a random effects model, so we can use the ...

Question: 9.4

In the article “Review of Development and Application of CRSTER and MPTER Models” (R. Wilson, Atmospheric Environment, 1993:41–57), several measurements of the maximum hourly concentrations (in 𝜇g/m³) of SO2 are presented for each of four power plants. The results are as follows (two outliers have ...

Verified Answer:

In the ANOVA table, the P-value for the null hypot...

Question: 9.17

In an emulsion liquid membrane system, an emulsion (internal phase) is dispersed into an external liquid medium containing a contaminant. The contaminant is removed from the external liquid through mass transfer into the emulsion. Internal phase leakage occurs when portions of the extracted ...

Verified Answer:

Using the sign table (Table 9.12), we compute esti...

Question: 9.15

Refer to Example 9.14. Construct an ANOVA table. For each effect and interaction, test the null hypothesis that it is equal to 0. Which factors, if any, seem most likely to have an effect on the outcome? ...

Verified Answer:

The ANOVA table follows. The sums of squares for t...

Question: 9.14

A 2³ factorial experiment was conducted to estimate the effects of three factors on the compressive strength of concrete cylinders. The factors were A: type of sand (fine or coarse), B: type of concrete (standard formulation or new formulation), and C: amount of water (low or high). Three ...

Verified Answer:

We use the sign table (Table 9.7) to find the appr...

Question: 9.13

The design suggested in Example 9.12 has been adopted, and the experiment has been carried out. The results (from MINITAB) follow. Does the output indicate any violation of necessary assumptions? What do you conclude regarding the effect of drill speed on excess diameter? ...

Verified Answer:

In a randomized complete block design, there must ...