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

Question

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

Quizplus · Accepted Answer

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.

Using the Following Information, Calculate the Z-Statistic for the Z-Test