Using the following information, calculate the z-statistic for the z-test for one mean. = 31.75 μ = 25.67 = 2.45

A) 2.48
B) -2.48
C) .10
D) -.10

The formula for the z-statistic for the z-test for one mean is:

z = (x̄ - μ) / (σ / √n)

where x̄ is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, we have:

x̄ = 31.75
μ = 25.67
σ = 2.45
n = unknown

We don't have the sample size, so we can't calculate the z-statistic exactly. However, we can still eliminate answer choices based on logical reasoning.

The z-statistic is a measure of how many standard deviations the sample mean is from the population mean. A positive z-statistic means the sample mean is above the population mean, while a negative z-statistic means the sample mean is below the population mean.

Given that the sample mean is 31.75 and the population mean is 25.67, it seems likely that the sample mean is higher than the population mean. Therefore, we would expect the z-statistic to be positive.

Answer choices C and D are both negative, so they can be eliminated.

Answer choice B is also negative, which means it's on the right track, but it's not the correct answer because the absolute value of the z-statistic should be around 2.5 (based on the difference between the sample mean and population mean), not 2.48.

That leaves answer choice A as the best option - it's positive and in the right neighborhood of 2.5.