Answer to Question #279446 in Statistics and Probability for Ashu

Question

sample of soil were prepared with varying amount of inorganic phosphorus. corn plant grown ineach soil were harvested after 8 days and analysed fir phosphorous contents. the objective was to see to what extent additional phosphorous in the soil increased the concentration of phosphorous in the plants. the data for 8 samples are as follows

Inorganic soil phosphorous (PPM) 1,4, 5, 9, 13, 11, 23. 23

Organic soil phosphorous (PPM) 64, 71, 54, 81, 93, 76, 77, 95

Answer 1

$\begin{aligned} &\sum \mathrm{e}^{2}=800.43 \\ &\text { Standard error, se } \left.=\sqrt{( \mathrm{E}^{2} /(\mathrm{n}-2)}\right)=\sqrt{(800.43 /(9-2))}=10.6933 \\ &\text { Standard error for slope, se(b1) }=\operatorname{se} / \sqrt{S Sx x} =10.6933 / \sqrt{734}={0.3947} \\ &\text { Null and alternative hypothesis: } \\ &\text { Ho: } \beta_{1}=0 ; \text { Ha: } \beta_{1} \neq 0 \\ &\text { Test statistic: } \\ &t=\text { b1/se(b1) }=1.42 / 0.3947=3.59 \\ &\text { df }=n-2=7 \\ &p \text {-value }=T . D I S T .2 T(A B S(3.5898), 7)=0.0089 \\ &\text { Conclusion: } \\ &p \text {-value }<\alpha, \text { Reject the null hypothesis. } \\ &\text { There is enough evidence to conclude that soil } P \text { is a useful predictor of corn } P . \end{aligned}$