Question

Four cars are for sale. The red car costs $15,000, the blue car costs $18,000, the green car costs $22,000, and the white car costs $20,000. Use the table to identify all possible samples of size n = 2 from this population and their sample means. The first sample is done for you.

Sample
n = 2 R, B R, G R, W B, G B, W G, W
Costs
($1000s) 15, 18 15, 22 15, 20 18, 22 18, 20 22, 20
Sample
Mean 16.5 18.5 17.5 20 19 21

What is the mean of all six sample means?

What is the value of the population mean?

Is the sample mean an unbiased estimator of the population mean?

Answer 1

First, let's calculate the mean for each of the given samples:

1. R, B: (15,000 + 18,000) / 2 = 16,500 (already given)

2. R, G: (15,000 + 22,000) / 2 = 18,500 (already given)

3. R, W: (15,000 + 20,000) / 2 = 17,500 (already given)

4. B, G: (18,000 + 22,000) / 2 = 20,000 (already given)

5. B, W: (18,000 + 20,000) / 2 = 19,000 (already given)

6. G, W: (22,000 + 20,000) / 2 = 21,000 (already given)

Now, let's calculate the mean of all six sample means:

(16,500 + 18,500 + 17,500 + 20,000 + 19,000 + 21,000) / 6 = 112,500 / 6 = 18,750

The mean of all six sample means is 18,750.

Next, let's calculate the population mean:

(15,000 + 18,000 + 22,000 + 20,000) / 4 = 75,000 / 4 = 18,750

The population mean is 18,750.

Since the mean of all six sample means is equal to the population mean (18,750), the sample mean is an unbiased estimator of the population mean.