Final answer:
Using the formula for the z-score, with a sample mean of 64, a null hypothesis mean of 67, a population standard deviation of 27, and a sample size of 63, the test statistic z is calculated to be approximately -0.8835.
Step-by-step explanation:
The question asks to compute the value of the test statistic z for a hypothesis test concerning a single population mean μ (mu).
To compute the z-score, you would use the formula:
z = (x - μ) / (σ / √n)
where x is the sample mean, μ is the population mean under the null hypothesis, σ is the population standard deviation, and n is the sample size.
Given that x = 64, μ = 67 (as per H0), σ = 27, and n = 63, the calculation for the test statistic z is:
z = (64 - 67) / (27 / √63)
z = -3 / (27 / 7.93725)
z = -3 / 3.39598
z = -0.8835
Therefore, the calculated test statistic z for the sample mean is approximately -0.8835.