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The following output summarizes portion of the results for two-way analysis of variance experiment with no interaction_ Factor A consists of five different kinds of...

Question

The following output summarizes portion of the results for two-way analysis of variance experiment with no interaction_ Factor A consists of five different kinds of organic fertilizers, factor B consists of three different kinds of soil acidity levels, and the variable measured is the height (in inches) of a plant at the end of four weeks_Find the missing values in the ANOVA table: (Round intermediate calculations to at least 4 decimal places_ Round MS" to 4 decimal places and "P to 3

The following output summarizes portion of the results for two-way analysis of variance experiment with no interaction_ Factor A consists of five different kinds of organic fertilizers, factor B consists of three different kinds of soil acidity levels, and the variable measured is the height (in inches) of a plant at the end of four weeks_ Find the missing values in the ANOVA table: (Round intermediate calculations to at least 4 decimal places_ Round MS" to 4 decimal places and "P to 3 decima places:) ANOVA Source of Variation MS p-value Rows 0.48 MSB Factor B 733 Columns 59.93 5.95 MSA MSE Factor A 0OO Error Total 66.36 b: At the 1% significance level, can you conclude that the average growth of the plant differs by organic fertilizer? Yes since the p-value for Factor A is less than significance level: Yes since the p-value for Factor A is greater than significance level: No since the p-value for Factor A is less than significance level. No since the p-value for Factor A is greater than significance level.



Answers

Preliminary data analyses indicate that use of a paired t-test is reasonable. Perform each hypothesis test by using either the critical-value approach or the P-value approach. Zea Mays. Charles Darwin, author of Origin of Species, investigated the effect of cross-fertilization on the heights of plants. In one study he planted 15 pairs of Zea mays plants. Each pair consisted of one cross-fertilized plant and one self-fertilized plant grown in the same pot. The following table gives the height differences, in eighths of an inch, for the 15 pairs. Each difference is obtained by subtracting the height of the self-fertilized plant the cross-fertilized plant, $$\begin{array}{rrrrr} \hline 49 & -67 & 8 & 16 & 6 \\ 23 & 28 & 41 & 14 & 29 \\ 56 & 24 & 75 & 60 & -48 \\ \hline \end{array}$$ a. Identify the variable under consideration. b. Identify the two populations. c. Identify the paired-difference variable. d. Are the numbers in the table paired differences? Why or why not? e. At the $5 \%$ significance level, do the data provide sulficient evidence to conclude that the mean heights of cross-fertilized and self-fertilized Zea mays differ? (Note: $d=20.93$ and $\left.s_{d}=37.74 .\right)$ f. Repeat part (e) at the $1 \%$ significance level.


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