Explanation:
We need to select the statement that is true about the survey conducted on 800 students regarding the number of automobiles in their household, given that the population mean is 2.7 automobiles with a standard deviation of 0.7.
A) The sample mean is equal to 2.7 automobiles.
B) The sample mean is greater than 2.7 automobiles.
C) The sample mean is less than 2.7 automobiles.
D) We cannot determine the sample mean from the information given.
To answer the question, we need to consider the concept of sampling distribution. The sampling distribution of the sample means is the distribution of all possible sample means that could be obtained from a given population. The central limit theorem states that as the sample size increases, the sampling distribution of the sample means approaches a normal distribution.
Since the sample size of 800 is large enough, we can use the central limit theorem to conclude that the sampling distribution of the sample means is approximately normal with a mean of 2.7 and a standard deviation of 0.7/sqrt(800), which is approximately 0.025.
Therefore, the statement that is true is:
A) The sample mean is equal to 2.7 automobiles.
This is because the sample mean is expected to be close to the population mean, which is 2.7 automobiles.