The assignment involves creating a scatter plot, calculating the correlation coefficient, stating hypotheses, testing the significance of the correlation, and explaining the relationship for given data on age and weekly jogging hours.
The given data represents the age of individuals and the corresponding hours they jog per week.
(a) Scatter Plot: A scatter plot can be drawn with ‘Age’ on the x-axis and ‘Hours’ on the y-axis. Each point on the plot represents an individual, with their age and jogging hours determining the location of the point.
(b) Correlation Coefficient: The correlation coefficient, often denoted by ‘r’, measures the strength and direction of a linear relationship between two variables. It can be calculated using a statistical formula or software tools. The value of ‘r’ ranges from -1 to 1, where -1 indicates a strong negative linear relationship, 1 indicates a strong positive linear relationship, and 0 indicates no linear relationship.
(c) State Hypothesis: The null hypothesis (H0) would be that there is no correlation between age and the number of hours a person jogs per week. The alternative hypothesis (H1) would be that there is a correlation.
(d) Test Significance: The significance of the correlation coefficient can be tested at α = 0.05. If the p-value is less than α, we reject the null hypothesis.
(e) Explain Relationship: Based on the results of the correlation coefficient and the significance test, we can explain the type of relationship between age and the number of hours a person jogs per week. If ‘r’ is positive, it means as age increases, the number of jogging hours also increases. If ‘r’ is negative, it means as age increases, the number of jogging hours decreases. If ‘r’ is close to 0, it means there is no linear relationship.