Maths-
General
Easy
Question
An ecologist selected a random sample of 30 prairie dogs from a colony and found that the mean mass of the prairie dogs in the sample was 0.94 kilograms (kg) with an associated margin of error of 0.12kg. Which of the following is the best interpretation of the ecologist's findings?
- All prairie dogs in the sample have a mass between 0.82 kg and 1.06 kg .
- Most prairie dogs in the colony have a mass between 0.82 kg and 1.06 kg .
- Any mass between 0.82 kg and 1.06 is a plausible value for the mean mass of the prairie dogs in the sample.
- Any mass between 0.82 and 1.06 is a plausible value for the mean mass of the prairie dogs in the colony.
Hint:
Hint:
A sample is called a random sample if every sample has an equal probability of being chosen. Margin of error expresses the difference between actual and predicted results in a random sample survey. In simpler terms, it is the degree of uncertainty our results from the sample survey might have. It is the amount added and subtracted from the given value to form an interval. Here, we have to verify each of the statements given in the option.
The correct answer is: Any mass between 0.82 and 1.06 is a plausible value for the mean mass of the prairie dogs in the colony.
Given,
Size of the sample = 30
Mean mass of the prairie dogs = 0.94 kilograms
Marginal error = 0.12 kg
So the interval in which the mean mass of the prairie dogs lie is given by
So, the mean mass of the prairie dogs in the random sample of 30 dogs lies between 0.82kg and 1.06kg.
But this does not mean that every dog in the sample has mass between 0.82kg and 1.06kg because, this quantity just represents the interval in which mean mass lies, not the mass of dogs.
Option A is incorrect.
Even though the sample is random, it is possible that the 30 dogs selected have some common trait regarding weight. So, most dogs in the colony may not have a mass between 0.82kg and 1.06kg.
Option B is incorrect.
Any mass between 0.82 kg and 1.06 kg is a plausible value for the mean mass of the prairie dogs in the sample.
Of course this statement is true, but it is not the best interpretation of the ecologist’s findings.
As we are taking a random sample from the colony, the above statement is true for the dogs in the colony too, not just the sample.
So, any mass between 0.82 kg and 1.06 kg is a plausible value for the mean mass of the prairie dogs in the colony.
Hence, the correct option is D)
Note:
There are many concepts and definitions used in solving this question. The student must be familiar with mean, sampling, random sample, margin of error and hoe any results derived from the sample relate to the population, to solve this problem correctly.
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