Students investigated the effect of a phosphate-enriched fertilizer on the growth of tomato seedlings.
(i) The students wanted to test whether there was a significant difference between the mean shoot lengths of the seedlings in Group A and Group B. State the name of the most appropriate statistical test for the students to use.
(ii) Justify your choice of statistical test given in part (i).
The students also categorized the root branching complexity of the seedlings in Group B into four distinct categories: Very Low, Low, Medium, and High. They used a chi-squared (χ2\chi^2χ2) test to determine whether the observed frequency distribution of these four categories differed significantly from their expected genetic ratio.
Their null hypothesis was: There is no significant difference between the observed and expected frequency distribution of root branching complexity in the seedlings.
The calculated chi-squared value was 8.508.508.50.
The students compared their calculated value to the critical values in the table below:
Degrees of freedom (df)p=0.10p=0.05p=0.0112.713.846.6424.605.999.2136.257.8211.3447.789.4913.2859.2411.0715.09 \begin{array}{|c|c|c|c|}\hline\text{Degrees of freedom } (df) & p = 0.10 & p = 0.05 & p = 0.01 \\ \hline 1 & 2.71 & 3.84 & 6.64 \\ \hline 2 & 4.60 & 5.99 & 9.21 \\ \hline 3 & 6.25 & 7.82 & 11.34 \\ \hline 4 & 7.78 & 9.49 & 13.28 \\ \hline 5 & 9.24 & 11.07 & 15.09 \\ \hline\end{array} Degrees of freedom (df)12345p=0.102.714.606.257.789.24p=0.053.845.997.829.4911.07p=0.016.649.2111.3413.2815.09What can the students conclude about their results based on a chi-squared value of 8.508.508.50?
