Question

1. The following are 30 time lapses in minutes between eruptions of Old Faithful geyser in Yellowstone National Park, recorded between the hours of 8 a.m. and 10 p.m. on a certain day, and measured from the beginning of one eruption to the beginning of the next:

68, 63, 66, 63, 61, 44, 60, 62, 71, 62, 62, 55, 62, 67, 73, 72, 55, 67, 68, 65,

60, 61, 71, 60, 68, 67, 72, 69, 65, 66

A researcher wants to use these data for inference purposes, but is concerned about whether it is reasonable to treat such data as a random sample. What do you think? Justify your answer.

Answer 1

The eruption times of a geyser are determined by a largely unknown distribution. The eruption times in fact depend upon the accumulation of water and steam bubbles in a side reservoir prior to the eruption. Hence, this is something which depends upon a lot of climatic and surrounding conditions.

Given the eruption times doesn't follow a well-defined distribution, we can't model and predict the eruption times with any reasonable level of accuracy. We simply cannot, with a high and consistent accuracy, predict the parameters of the underlying population (the set of all eruption times). Hence, it is very reasonable to think the sample is a random sample.