Question

7 8 9 10 11 9 8 7 12 13 14 9 11 18 20 6 10 19 9

For the following questions:
μ = 9.00 and σ = 3.00.
Assume that the population data are normally distributed.
Calculate the z-score for sample means (single-sample z-test).
Show your calculations.

Answer 1

To calculate the z-score for a sample mean, use the formula z = (x - μ) / (σ / √n), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Step-by-step explanation:

The z-score for a sample mean can be calculated using the formula:

z = (x - μ) / (σ / √n)

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

For example, to calculate the z-score for a sample mean of 76 when the population mean is 9.00 and the population standard deviation is 3.00:

z = (76 - 9.00) / (3.00 / √n)

Let's assume n = 20. Plugging in the values:

z = (76 - 9.00) / (3.00 / √20)

z = 67 / (3.00 / √20)

z = 67 / (3.00 / 4.47)

z = 67 / 0.672

z ≈ 99.85

Therefore, the z-score for a sample mean of 76 is approximately 99.85.