Maths-
General
Easy
Question
To determine the mean number of children per household in a community, Tabitha surveyed 20 families at a playground. For the 20 families surveyed, the mean number of children per household was 2.4. Which of the following statements must be true?
- The mean number of children per household in the community is 2.4.
- A determination about the mean number of children per household in the community should not be made because the sample size is too small.
- The sampling method is flawed and may produce a biased estimate of the mean number of children per household in the community.
- The sampling method is not flawed and is likely to produce an unbiased estimate of the mean number of children per household in the community.
Hint:
To solve this problem, we should have a understanding of sampling techniques and concept of biased and unbiased estimators.
The correct answer is: A determination about the mean number of children per household in the community should not be made because the sample size is too small.
Step 1 of 2:
Tabitha surveyed 20 families at a playground. For the 20 families surveyed, the mean number of children per household was 2.4
Now, there is a huge number of family compared to the 20 families at the playground. So, that sample size is too small in this case.
Step 2 of 2:
The families taken account in the sample is a specific age group of people. So, the formula used to calculate the mean for the sample may not be a good fit for the calculation of population mean children per household. Hence, that would create bias.
Final Answer:
The right choices are in this case—
B) A determination about the mean number of children per household in the community should not be made because the sample size is too small.
C) The sampling method is flawed and may produce a biased estimate of the mean number of children per household in the community.
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