To test if the three soils produce the same mean height of bean plants, a one-way ANOVA test at a 3 percent level of significance can be performed. If the p-value is less than 0.03, it can be concluded that the heights are different.
Step-by-step explanation:
To determine if the three soils produce the same mean height, we can perform a one-way ANOVA test at a 3 percent level of significance. The null hypothesis is that the mean heights of plants grown in the three soils are equal, while the alternative hypothesis is that they are different.
Using the ANOVA test, we calculate the p-value, which measures the strength of evidence against the null hypothesis. If the p-value is less than the significance level of 0.03, we can reject the null hypothesis and conclude that there is evidence of a difference in mean heights.
In this case, we would calculate the p-value using statistical software or a calculator. If the p-value is less than 0.03, we would reject the null hypothesis and conclude that the heights of the bean plants grown in the three soils are different.