Suppose that 25% of all Sydneysiders catch the train to work.

You work for a market research company and are interested in the proportion of Sydneysiders who catch the train to work.

As part of your research, you go to the local train station and survey 100 commuters, finding that 45% catch the train to work.

Correctly identify the:
1: Parameter
2: Estimate/Statistic

Question

Suppose that 25% of all Sydneysiders catch the train to work.

You work for a market research company and are interested in the proportion of Sydneysiders who catch the train to work.

As part of your research, you go to the local train station and survey 100 commuters, finding that 45% catch the train to work.

Correctly identify the:
1: Parameter
2: Estimate/Statistic

BlackTom AI · Accepted Answer

We start by identifying what is being asked in this matching question. The task is to match two concepts: (1) the parameter, which is a fixed population value, and (2) the estimate/statistic, which is derived from the sample data.

Option by option analysis:

- 0.45: This value represents the proportion of the 100 commuters in the sample who catch the train to work. It is derived from the data collected and serves as a point estimate of the population proportion. In statistical terms, this is the sample proportion (often denoted p-hat). Since a statistic is a quantity calculated from the sample, this value correctly corresponds to the estimate/statistic.

- sqrt(0.25 * 0.45): This expression computes a square root of a product involving 0.25 and 0.45. It does not represent a standard population parameter or a standard error in this context, and it does not align with the definitions of parameter or statistic here. As such, this option is not a correct match for either the parameter or the statistic in this problem. The units and meaning are unclear for this context, making it an incorrect choice.

- sqrt(0.25 * 0.45) / 100: This simplifies to (sqrt(0.25 * 0.45)) divided by 100. Again, this does not correspond to the population proportion (which is a fixed value) nor to the sample proportion (which is a simple ratio of successes to trials, not a scaled square-root expression). It misrepresents both the parameter and the statistic, so it is incorrect.

- 100: This is a count (the sample size in this problem) and does not itself represent the population proportion nor the observed sample proportion. While the sample size is an important quantity in determining the precision of estimates, it is not the parameter or the estimate/statistic. Therefore, this option is not a correct match.

- 0.25: This is the stated population proportion in the problem (the true proportion of Sydneysiders who catch the train to work). In statistical terms, this is the parameter. It correctly matches the concept of the parameter rather than the sample-derived statistic.

In summary, when distinguishing between parameter and statistic in this scenario, 0.25 is correctly identified as the parameter, and 0.45 is correctly identified as the estimate/statistic. The remaining expressions do not align with either definition given the context of the question.

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