An environmental scientist is investigating the relationship between daily sunlight exposure and the concentration of Vitamin K in a specific species of mountain herb. The scientist has access to a population of 180 herbs in a controlled conservatory.
Describe how the scientist should select a random sample of 10 herbs from the population.
The scientist recorded the average daily sunlight exposure (in hours) over a month for the 10 herbs. The herbs were then ranked based on their Vitamin K concentration, with 1 representing the highest concentration and 10 the lowest. The results are shown in the table below:
HerbABCDEFGHIJVitamin K Rank12345678910Sunlight Exposure (h)12.213.010.511.18.89.27.57.95.86.4 \begin{array}{|l|c|c|c|c|c|c|c|c|c|c|} \hline \text{Herb} & A & B & C & D & E & F & G & H & I & J \\ \hline \text{Vitamin K Rank} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline \text{Sunlight Exposure (h)} & 12.2 & 13.0 & 10.5 & 11.1 & 8.8 & 9.2 & 7.5 & 7.9 & 5.8 & 6.4 \\ \hline \end{array} HerbVitamin K RankSunlight Exposure (h)A112.2B213.0C310.5D411.1E58.8F69.2G77.5H87.9I95.8J106.4Calculate Spearman's rank correlation coefficient for these data.
The scientist believes that herbs receiving more sunlight exposure will have a higher concentration of Vitamin K. Test this belief at the 5% significance level. State your hypotheses clearly. (The critical value for n=10n=10n=10 at the 5% level of significance is 0.5636).
