Question

Amy bought a packet of 50 balloons before her friends birthday an counted there were 15 red, 15 green, 10 yellow, and 10 blue balloons in the packet. From her previous experience she suspected that green and blue colored balloons probably take higher time to inflate than red and yellow balloons. To check if her suspicion is right she hired a friend to blow up the balloons over two days before the birthday and she measured the time needed to inflate the balloons with a stopwatch in each case.

(a) Identify all sources of variation in Amy’s experiment. (b) What is the response and treatment in the experiment? (c) Based on the possible sources of variation do you think the CRD model is a good choice? Why or why not? (d) Write down a complete mathematical model that you think would be suitable, explaining all notations and mentioning all possible values of i,j etc. (e) Do you think the assumption that the errors follow iid normal(0, σ2 ) might be violated in the experiment?

Answer 1

(a) Between variation of time needed to inflate the four different color balloons, within variation of time needed to inflate each of four different color balloons and total variation i.e. Between variation means variation due to use of different color of balloons where as within variation is due to chance causes or random causes.

(b) Response: time needed to inflate the balloons

Treatment: 4 colors of balloons i.e. red, green, yellow, blue

(c) Yes, since here variation in response is only due to use of different colors of balloons and hence we eleminate heterogenity in one direction. Theorefore one way ANOVA is appropriate and CRD is used.

(d)

Response: