Five strains of the Staphylococcus aureus bacteria were grown at 35 degrees Celsius for 24 hours in a culture broth containing either 0.6% of the nutrient tryptone or 1% of tryptone. We want to know if these two tryptone concentrations affect the growth of S. aureus in culture. Here are the resulting bacterial counts for each condition and bacterial strain: $\begin{array} { l l l l l l } & \text { Strain 1 } & \text { Strain 2 } & \text { Strain3 } & \text { Strain 4 } & \text { Strain 5 } \\\mathbf { 0 . 6 \% } \% \text { tryptone } & 66 & 71 & 93 & 102 & 62 \\\mathbf { 1 } \% \text { tryptone } & 147 & 63 & 89 & 106 & 98\end{array}$
We choose to analyze these data using the Wilcoxon signed rank test.
If the bacterial counts have a continuous distribution that is not affected by the different treatments, then what is the mean of the Wilcoxon signed rank test statistic, W⁺?

Question

Five strains of the Staphylococcus aureus bacteria were grown at 35 degrees Celsius for 24 hours in a culture broth containing either 0.6% of the nutrient tryptone or 1% of tryptone. We want to know if these two tryptone concentrations affect the growth of S. aureus in culture. Here are the resulting bacterial counts for each condition and bacterial strain:

\begin{array} { l l l l l l } & \text { Strain 1 } & \text { Strain 2 } & \text { Strain3 } & \text { Strain 4 } & \text { Strain 5 } \\\mathbf { 0 . 6 \% } \% \text { tryptone } & 66 & 71 & 93 & 102 & 62 \\\mathbf { 1 } \% \text { tryptone } & 147 & 63 & 89 & 106 & 98\end{array}

We choose to analyze these data using the Wilcoxon signed rank test.
If the bacterial counts have a continuous distribution that is not affected by the different treatments, then what is the mean of the Wilcoxon signed rank test statistic, W⁺?

Quizplus · Accepted Answer

The Answer of Five strains of the Staphylococcus aureus bacteria were grown at 35 degrees Celsius for 24 hours in a culture broth containing either 0.6% of the nutrient tryptone or 1% of tryptone. We want to know if these two tryptone concentrations affect the growth of S. aureus in culture. Here are the resulting bacterial counts for each condition and bacterial strain: $$\begin{array} { l l l l l l } & \text { Strain 1 } & \text { Strain 2 } & \text { Strain3 } & \text { Strain 4 } & \text { Strain 5 } \ \mathbf { 0 . 6 \% } \% \text { tryptone } & 66 & 71 & 93 & 102 & 62 \ \mathbf { 1 } \% \text { tryptone } & 147 & 63 & 89 & 106 & 98 \end{array}$$ We choose to analyze these data using the Wilcoxon signed rank test. If the bacterial counts have a continuous distribution that is not affected by the different treatments, then what is the mean of the Wilcoxon signed rank test statistic, W⁺?

Five Strains of the Staphylococcus Aureus Bacteria Were Grown at 35