Question 1183001: The average lifespan of a Ghanaian is 57years. The average lifespan of males in Ghana is known to be 55 years while the average lifespan of females in Ghana is known to be 60 years. The average lifespan of people from the Northern region of Ghana is known to be 58 years while the average lifespan of people in the East region of Ghana is known to be 54 years.
Use the above information to answer the following questions:
(i).With your reasons, discuss all possible population parameters from the above information.
(ii).With your reasons, discuss all possible sample statistics from the above information.
(iii) Compare and contrast the average lifespan of males and females. Which group average is more likely to represent the corresponding population parameter? Give reasons for your answer.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's break down the given information and address the questions:
**(i) Population Parameters:**
A population parameter is a characteristic of an *entire* population. From the given information, we have the following population parameters:
* **Average lifespan of all Ghanaians:** 57 years. This is a parameter because it represents the entire population of Ghana.
* **Average lifespan of Ghanaian males:** 55 years. This is a parameter as it refers to the entire sub-population of males in Ghana.
* **Average lifespan of Ghanaian females:** 60 years. This is a parameter because it refers to the entire sub-population of females in Ghana.
* **Average lifespan of people from the Northern region of Ghana:** 58 years. This is a parameter as it refers to the entire population of the Northern region.
* **Average lifespan of people from the Eastern region of Ghana:** 54 years. This is a parameter as it refers to the entire population of the Eastern region.
It's important to note that these are *stated* population parameters. In real-world scenarios, these values would likely be *estimates* based on samples, and the true population parameters would be unknown.
**(ii) Sample Statistics:**
Sample statistics are characteristics calculated from a *sample* of the population. The provided information *does not give us any sample statistics*. We are only given population averages. If we had taken, say, a random sample of 100 Ghanaians and calculated their average lifespan, that average would be a sample statistic. Similarly, if we took a sample of 50 males from the Northern region and found their average lifespan, that would be a sample statistic.
**Why no sample statistics are given:** The problem states things like "The *average* lifespan of males in Ghana *is known to be* 55 years." This phrasing indicates that the value is believed to be a population parameter (or at least treated as such), not something calculated from a sample.
**(iii) Comparing Male and Female Lifespans:**
* **Comparison:** The average lifespan of females (60 years) is higher than the average lifespan of males (55 years) in Ghana. The difference is 5 years.
* **Which average is more likely to represent the population parameter?**
It's impossible to say definitively which group average is *more* likely to represent the true population parameter without more information (like the sample size and standard deviation if these were sample means). However, we can discuss the factors that influence the accuracy of a sample statistic as an estimate of a population parameter:
* **Sample Size:** Larger samples generally lead to more accurate estimates. If the male and female lifespan averages were calculated from samples, the larger of the two samples would provide a more reliable estimate.
* **Representativeness of the Sample:** The sample should be a random and representative sample of the population. Bias in sampling can lead to inaccurate estimates.
* **Variability within the Population:** If there is a lot of variation in lifespans within each gender group, a larger sample would be needed to get a precise estimate of the average.
**Since we are told that the values are known, we are to assume they are correct population parameters. Therefore, they both perfectly represent the corresponding population parameter.**
**In summary:** Without information about the sample sizes and how the averages were determined (if they were from samples), we can only compare the stated average lifespans and acknowledge that both are stated as population parameters.
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