Using the following information, calculate the z-statistic for the z-test for one mean. = 27 μ = 15 = 1.50

A) -8.00
B) 8.00
C) 4.00
D) -.10

To calculate the z-statistic, we use the formula: z = (x - μ) / (σ / sqrt(n)), where x 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 are given x = 27, μ = 15, and σ = 1.50. We are not given the sample size, so we cannot calculate the standard error directly.

However, if we assume that the sample size is large enough (i.e. n > 30), we can use the central limit theorem and approximate the distribution of sample means to a normal distribution with a standard error of σ / sqrt(n).

Assuming a large enough sample size, the z-statistic is:
z = (27 - 15) / (1.5 / sqrt(n))
z = 12 / (1.5 / sqrt(n))
z = 8 * sqrt(n)

Since we do not know n, we cannot calculate the exact value of the z-statistic. However, we can see that the z-statistic is positive and large, which indicates that the sample mean is significantly higher than the population mean. Therefore, the best choice is B, 8.00.