You work for a financial information website. You draw a random sample of 100 subscribers and determine that their mean income is $68,500. Which statement is true?
A)
You conclude that the income of all subscribers is $68,500.
B)
You conclude that half of the subscribes earn less than $68,500.
C)
You conclude that half of the subscribes earn more than $68,500.
D)
You conclude that the mean income of all subscribers is close to $68,500.
Clearly, it is D.
You use random samples to estimate properties of the whole population.
aye steve
You work for a financial information website. You draw a random sample of 100 subscribers and determine that their mean income is $68,500. Which statement is true?
A market researcher selected 200 people at random from a group of people who indicated that they liked a certain book. The 200 people were shown a movie based on the book and then asked whether they liked or disliked the movie. Of those surveyed, 95% said they disliked the movie. Which inferences can appropriately be drawn from this survey result?
Well, well, well, looks like someone's got some financial data on their hands! Let me put on my thinking cap, or should I say, thinking hat, to help you out.
Now, here's the deal: the statement that is true is D) You conclude that the mean income of all subscribers is close to $68,500. Why? Well, you took a random sample of subscribers and found that the mean income of this group is $68,500. This gives you a good estimate of the average income among the subscribers, but it doesn't necessarily mean that every single subscriber has an income of exactly $68,500. It just means that the mean income of all subscribers is likely to be close to that figure.
So, don't go jumping to conclusions about everyone's income being the same or half the subscribers earning more or less than $68,500. Stick with the statement that says the mean income is close to $68,500, and you'll be on the right track. Happy number crunching!
To determine which statement is true, we need to understand the concept of a random sample and how it represents the population.
A random sample is a subset of individuals selected from a larger population, with the aim of representing the characteristics of that population. In this case, the sample consists of 100 subscribers from the financial information website.
Now, let's analyze each statement:
A) You conclude that the income of all subscribers is $68,500.
This statement is not necessarily true. The mean income of the sample may provide an estimate of the true mean income of all subscribers, but it does not guarantee that every subscriber's income is exactly $68,500. The sample mean of $68,500 is an estimate of the population mean income.
B) You conclude that half of the subscribers earn less than $68,500.
This statement is not necessarily true. The mean income only provides information about the average income, but it does not reflect the distribution of incomes within the sample or the population. It is possible that more than half or less than half of the subscribers earn less than $68,500.
C) You conclude that half of the subscribers earn more than $68,500.
This statement is not necessarily true. Similar to statement B, the mean income only reflects the average income, not the distribution of incomes within the sample or the population. It is possible that more than or less than half of the subscribers earn more than $68,500.
D) You conclude that the mean income of all subscribers is close to $68,500.
This statement is the most accurate from the given options. Since the mean income of the sample is $68,500, it is reasonable to assume that the mean income of the population (all subscribers) is close to $68,500. However, without additional statistical tests, we cannot definitively conclude that the mean income of the population is exactly $68,500.
In summary, option D) is the most accurate statement considering the information provided.