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plete the sentences to state the decision and conelusion of the hertieulturist's tast. fail to reject null hypothesis The decision is to the at a significance level of at least one of the population means is insufficient a = 0.01. There is evidence to conclude that different from at least one other population mean

plete the sentences to state the decision and conelusion of the hertieulturist's tast. fail to reject null hypothesis The decision is to the at a significance level of at least one of the population means is insufficient a = 0.01. There is evidence to conclude that different from at least one other population mean

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Word Bank:

Reject

The population mean of species 4

All the other population means 

The population mean of species 3

fail to accept 

sufficient 

alternative hypothesis

the population mean of species 2 

each of the population means

the same as 

the population mean fo species 1

accept 

fail to reject 

null hypothesis 

insufficient 

at least one of the population means 

different from

at least one other population mean

### ANOVA Table | Source of Variation | SS | df | MS | f | P-value | f-critical | |---------------------|---------|----|---------|-------|---------|------------| | Between groups | 169.057 | 3 | 56.352 | 5.398 | 0.002 | 4.050 | | Within groups | 793.330 | 76 | 10.439 | | | | | Total | 962.386 | 79 | | | | | This table represents the results of an ANOVA (Analysis of Variance) test. The “Between groups” row shows the variation due to interaction between the different groups, while the “Within groups” row shows variation within each group. The total variation is the sum of these two. The f-value and P-value help to determine the statistical significance of the results. ### Sentence Completion Exercise Complete the sentences to state the decision and conclusion of the horticulturist's test: - **The decision is to**: reject the null hypothesis at a significance level of α = 0.01. - **There is**: sufficient evidence to conclude that at least one of the population means is different from at least one other population mean. ### Answer Bank - fail to reject - reject - the null hypothesis - α = 0.01 - insufficient - sufficient - different from - at least one other population mean - at least one of the population means - all of the other population means - the population mean of species 3 - the population mean of species 4 This exercise involves selecting the appropriate terms from the answer bank to complete the sentences correctly based on the ANOVA test results.
Transcribed Image Text:### ANOVA Table | Source of Variation | SS | df | MS | f | P-value | f-critical | |---------------------|---------|----|---------|-------|---------|------------| | Between groups | 169.057 | 3 | 56.352 | 5.398 | 0.002 | 4.050 | | Within groups | 793.330 | 76 | 10.439 | | | | | Total | 962.386 | 79 | | | | | This table represents the results of an ANOVA (Analysis of Variance) test. The “Between groups” row shows the variation due to interaction between the different groups, while the “Within groups” row shows variation within each group. The total variation is the sum of these two. The f-value and P-value help to determine the statistical significance of the results. ### Sentence Completion Exercise Complete the sentences to state the decision and conclusion of the horticulturist's test: - **The decision is to**: reject the null hypothesis at a significance level of α = 0.01. - **There is**: sufficient evidence to conclude that at least one of the population means is different from at least one other population mean. ### Answer Bank - fail to reject - reject - the null hypothesis - α = 0.01 - insufficient - sufficient - different from - at least one other population mean - at least one of the population means - all of the other population means - the population mean of species 3 - the population mean of species 4 This exercise involves selecting the appropriate terms from the answer bank to complete the sentences correctly based on the ANOVA test results.
**Analysis of Shrub Species Growth Rates in a Greenhouse Environment** This study examines the aboveground height growth rates of four different ornamental shrub species cultivated in a controlled greenhouse setting. To ensure an unbiased representation and to prevent any environmental factors from affecting the results, shrubs were sourced from a random seed sample. Each shrub was planted in identical soil mixtures and pot sizes, with the position of pots randomized throughout the greenhouse. ### Data Summary The table below outlines the findings of the growth rate measurement for each shrub species: | Population | Population Description | Sample Size | Sample Mean (cm/year) | Sample Standard Deviation (cm/year) | |------------|------------------------|-------------|----------------------|------------------------------------| | 1 | Species 1 | \( n_1 = 20 \) | \( \bar{x}_1 = 13.749 \) | \( s_1 = 2.160 \) | | 2 | Species 2 | \( n_2 = 20 \) | \( \bar{x}_2 = 16.619 \) | \( s_2 = 4.284 \) | | 3 | Species 3 | \( n_3 = 20 \) | \( \bar{x}_3 = 13.608 \) | \( s_3 = 3.396 \) | | 4 | Species 4 | \( n_4 = 20 \) | \( \bar{x}_4 = 12.769 \) | \( s_4 = 2.683 \) | ### Statistical Analysis The growth rate distributions for each sample were found to be approximately normal, with no evidence of outliers. A one-way analysis of variance (ANOVA) was employed at a significance level of \( \alpha = 0.01 \) to evaluate whether there were statistically significant differences in the mean growth rates among the four species. This study's methodological approach ensures reliable results by considering the effects of environmental variability, thus contributing to an accurate understanding of species-specific growth rates in ornamental shrubs.
Transcribed Image Text:**Analysis of Shrub Species Growth Rates in a Greenhouse Environment** This study examines the aboveground height growth rates of four different ornamental shrub species cultivated in a controlled greenhouse setting. To ensure an unbiased representation and to prevent any environmental factors from affecting the results, shrubs were sourced from a random seed sample. Each shrub was planted in identical soil mixtures and pot sizes, with the position of pots randomized throughout the greenhouse. ### Data Summary The table below outlines the findings of the growth rate measurement for each shrub species: | Population | Population Description | Sample Size | Sample Mean (cm/year) | Sample Standard Deviation (cm/year) | |------------|------------------------|-------------|----------------------|------------------------------------| | 1 | Species 1 | \( n_1 = 20 \) | \( \bar{x}_1 = 13.749 \) | \( s_1 = 2.160 \) | | 2 | Species 2 | \( n_2 = 20 \) | \( \bar{x}_2 = 16.619 \) | \( s_2 = 4.284 \) | | 3 | Species 3 | \( n_3 = 20 \) | \( \bar{x}_3 = 13.608 \) | \( s_3 = 3.396 \) | | 4 | Species 4 | \( n_4 = 20 \) | \( \bar{x}_4 = 12.769 \) | \( s_4 = 2.683 \) | ### Statistical Analysis The growth rate distributions for each sample were found to be approximately normal, with no evidence of outliers. A one-way analysis of variance (ANOVA) was employed at a significance level of \( \alpha = 0.01 \) to evaluate whether there were statistically significant differences in the mean growth rates among the four species. This study's methodological approach ensures reliable results by considering the effects of environmental variability, thus contributing to an accurate understanding of species-specific growth rates in ornamental shrubs.
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