Consider the daily demand for bicycles at kiosks in DC. Below are side-by-side b
ID: 3255427 • Letter: C
Question
Consider the daily demand for bicycles at kiosks in DC. Below are side-by-side box plots of the distributions of demand for each day of the week. What about this plot suggests that there may be an association between Day and Demand? The F statistic has been calculated for this data, and it turns out it is 4.7. What is the practical interpretation of this number? Below is the sampling distribution of F for 5000 samples when no association exists between Day and Demand. Is the observed association statistically significant? Management only cares whether the demands vary from day to day by about 1000. Thus, does the association carry any practical significance?Explanation / Answer
Answer to part a)
The plot doesnot suggest any relation in the days and demand of cycle
there is no drastic difference in the ranges or means of the demand data based on the days
.
Answer to part b)
The F value is a ratio that tells us about the statistical difference. A value of F close to 1 indicates no statistical difference . Whereas a value of F very large indicates significant statistical difference.
We can also find the P value for this value of F 4.7 , with numebrator df = 1 , and denominator df = 6
we get P = 0.07
Since P value 0.07 > alpha 0.05 , thus we fail to reject the null and conclude that the demand does not depend on days
.
Answer to part c)
The histogram shows the value of F
The histogram is right skewed, which means that most of the F values are smaller, and very few F values touch the higher range
this indicates that the association between day and demand as indicated by some rare hiher F values is only by chance and thus there exists no relation between demand and days
.
Answer to part d)
If the management only finds the dependence of demand on day significant when there is a variation of about 1000 units, in that case we only compare the mean vlaues of the boxplots for each of the days , and we find that the means are again almost the same. The difference between the means doesnot exceed 1000 units on any of the days. Thus for the management as well the decision remains the same that the demand does not depend on the days.