a horticulturist measures the aboveground height growth rate of four different o

Question

a horticulturist measures the aboveground height growth rate of four different ornamental shrub species grown in a seeds, and they were all grown in the same soil mixture and in greenhouse. The the same size pot. To ensure that any slight differences in the environmental conditions throu confounded with species, she randomizes the location of the pots throughout the greenhouse. The table contains a surnmary of shrubs were grown from a random sample of hout the preenhouse are net her data Population Sample Population description size Sample mean Sample standard deviation Species 2017.153 cmv/ycar 2.666 cm/year Species 2 m 20 13.983 cmlyear -3.605 cm/year Species 3 20 15.120 cm/ycar3.774 cm/ycar Species 4 n-20-4 = 14.328 cmycar s-3.011cm/year The growth rate distributions of each sample are approximately normal, and the data do not contain outliers. The horticulturist uses a one way analysis of variance (ANOVA) at a significance level of -0.05 to 1 st if the mean growth rates of all for species are equal. Her results are shown in the table. Source of variation Between groups Within groups Tolal SS dr MS p-value f-critical 120.988 3 40.329 3.716 0.015 824.710 76 10.851 945.697 79 2.725

Explanation / Answer

Remember:

In the majority of analyses, an alpha of 0.05 is used as the cutoff for significance. If the p-value is less than 0.05, we reject the null hypothesis that there's no difference between the means and conclude that a significant difference does exist.

Here p = 0.015 which is less than 0.05

So,

Null is rejected

Thus,

Decision is to reject the null. There is insufficent evidence to conclude that growth rates of all four species are equal. (or atleast one mean is equal)

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