IB Maths AI SL Topic 4: Statistics and probability questions

Use a graphic display calculator to find Spearman’s rank correlation coefficient, $r_s$ for these data. Give your answer to three significant figures.

Interpret your value of $r_s$ in the context of the fieldwork.

The scatter plot suggests an overall increasing, curved relationship between distance from the road and the number of native plant species. State which coefficient, Pearson’s product moment correlation coefficient or Spearman’s rank correlation coefficient, is more appropriate for describing this relationship. Give a reason.

If one additional observation is an extreme value, explain how Pearson’s product moment correlation coefficient and Spearman’s rank correlation coefficient are likely to differ in their sensitivity to it.

Use a graphic display calculator to find Spearman’s rank correlation coefficient, $r_s$ for these data. Give your answer to three significant figures.

State the direction of the association indicated by $r_s$

If the researchers want to assess a linear relationship, rather than a monotonic relationship in general, name the more appropriate coefficient: Pearson’s product-moment correlation coefficient or Spearman’s rank correlation coefficient.

Plot F appears to be an outlier. State which of these two coefficients is generally less sensitive to an outlier.

State the null hypothesis, $H_0$ and the alternative hypothesis, $H_1$ for a test of whether moth detection and habitat type are independent.

Assuming $H_0$ is true, calculate the expected frequency of quadrats in habitat B in which moths are detected. Give your answer to 3 significant figures.

Use a GDC to carry out an appropriate test of independence using the frequencies in Figure 1. Give the $\chi^2$ statistic and the $p$-value, each to 3 significant figures.

Hence state the conclusion of the test at the 5% significance level, in the context of the fieldwork.