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.
The researcher is interested in testing the following one-sided test:
H₀: Bacterial counts with 0.6% and 1% tryptone have the same distribution.
H_a: Bacterial counts are systematically higher in one condition than the other.
Using the Normal approximation, what is the P-value for the Wilcoxon signed rank test, 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.
The researcher is interested in testing the following one-sided test:
H₀: Bacterial counts with 0.6% and 1% tryptone have the same distribution.
H_a: Bacterial counts are systematically higher in one condition than the other.
Using the Normal approximation, what is the P-value for the Wilcoxon signed rank test, W⁺?

Quizplus · Accepted Answer

The Wilcoxon signed rank test compares the differences between paired observations. The differences between the bacterial counts for each strain are calculated and ranked. The sum of the positive ranks (W+) is compared to the expected value under the null hypothesis. Given the data, the differences do not show a systematic increase in one condition over the other, leading to a P-value greater than 0.10.

Five Strains of the Staphylococcus Aureus Bacteria Were Grown at 35