Using the following information, calculate the z-statistic for the z-test for one mean. = 15 μ = 22 = 3.50
A) 2.00
B) -2.00
C) 1.23
D) -3.13

Question

Using the following information, calculate the z-statistic for the z-test for one mean.  = 15 μ = 22  = 3.50
A) 2.00 
B) -2.00 
C) 1.23 
D) -3.13

Quizplus · Accepted Answer

The formula for z-statistic 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.

From the given information, we have:

x̄ = 15
μ = 22
σ is unknown
n = 3.50

Since we do not have the population standard deviation, we cannot calculate the z-statistic directly. Therefore, we need to use a t-test with degrees of freedom (df) = n - 1 = 2.

The t-statistic can be calculated as:

t = (x̄ - μ) / (s / √n)

where s is the sample standard deviation.

From the given information, we have:

s = 3.50

Therefore,

t = (15 - 22) / (3.50 / √3) = -3.13

Using a t-distribution table with df = 2, we find that the two-tailed critical value at α = 0.05 is approximately 4.303.

Since the calculated t-value (-3.13) is less than the critical value (-4.303), we reject the null hypothesis and conclude that the sample mean is significantly different from the population mean at α = 0.05.

To convert this result to a z-statistic, we can use the relationship between t and z:

z = t / √df

Substituting the values, we get:

z = -3.13 / √2 = -2.22

Therefore, the z-statistic for the z-test for one mean is -2.22, which is closest to choice B (-2.00).

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