A. Mr. Russo exchanged 200 euros (European money ) for 270 dollars. How many dolla would he get for 300 euros?
B. Another name for sampling error is variability due to chance errors due to invalid measurement heterogeneity of variance homogeneity of variance
The correct answer and explanation is:
A. Exchange Rate Calculation:
To find how many dollars Mr. Russo would get for 300 euros, we first need to determine the exchange rate from euros to dollars.
Given:
- 200 euros = 270 dollars
The exchange rate can be calculated as: Exchange rate=270 dollars200 euros=1.35 dollars per euro\text{Exchange rate} = \frac{270 \text{ dollars}}{200 \text{ euros}} = 1.35 \text{ dollars per euro}
Now, to find how many dollars Mr. Russo would get for 300 euros: Dollars for 300 euros=300 euros×1.35 dollars per euro=405 dollars\text{Dollars for 300 euros} = 300 \text{ euros} \times 1.35 \text{ dollars per euro} = 405 \text{ dollars}
So, Mr. Russo would get 405 dollars for 300 euros.
B. Sampling Error Explanation:
The correct answer to the question is “variability due to chance”.
Sampling error is the difference between a sample statistic (such as the sample mean) and the corresponding population parameter (such as the population mean) that occurs due to random chance. It’s a natural part of statistical inference, occurring because no sample can perfectly represent the population. Here’s an explanation of why “variability due to chance” is the correct term:
- Sampling error is inevitable: Whenever a sample is drawn from a population, there’s a chance the sample won’t fully represent the population. This difference arises from the random selection process. For instance, a sample might over-represent some characteristics or under-represent others just by chance.
- Chance plays a crucial role: In a random sampling process, different samples drawn from the same population can produce slightly different results. This variability is what we call sampling error. This error is expected and normal, as it is driven purely by the randomness inherent in the sampling process.
- Sampling error versus systematic error: It is important to distinguish between sampling error and systematic error. Systematic error refers to biases or errors in measurement or sampling methods that can lead to consistent inaccuracies in the data. In contrast, sampling error is purely random and can be reduced by increasing sample size or improving sampling methods.
- Consequences of sampling error: The impact of sampling error decreases as sample size increases. With larger samples, the variability due to chance becomes smaller, and the sample statistic becomes closer to the population parameter. This principle is part of the law of large numbers in statistics.
- Variability in data: The phrase “variability due to chance” encapsulates the essence of sampling error. It acknowledges that the observed differences are not due to an error in measurement but rather the natural fluctuation that happens when selecting different samples from a larger population.
In conclusion, sampling error is the variability that arises due to chance and is not a flaw in the study but a natural part of the statistical process.