Question

select the correct answer.

a group of crafters is collecting data on the amount of yarn they use for each scarf knitted. each person collected 12 pieces of data and will compile that data to determine a population mean. one crafter, chris, has a sample mean of 200 meters of yarn.

which statement must be true about this situation?

• the population mean is also 200.
• there is not enough information to make a conclusion about the population mean.
• the population mean must be less than 200.
• the population mean must be greater than 200.

Explanation:

Analyze the relationship between sample mean and population mean

A sample mean \(\bar{x} = 200\) is an estimate of the population mean \(\mu\), but it does not determine the exact value of \(\mu\).

Evaluate the statements

Without data from the other crafters or the entire population, the exact population mean cannot be calculated or bounded.

Determine the correct option

Therefore, there is not enough information to make a definitive conclusion about the population mean.

Answer:

• The population mean is also 200.
• There is not enough information to make a conclusion about the population mean. (Correct answer)
• The population mean must be less than 200.
• The population mean must be greater than 200.