Step 1
(a) Find the value of the test statistic.
A sample of 75 items provided a mean of 18.32. The standard deviation of the entire population is given to be 2. The hypotheses are given below.
H0: μ ≥ 19
Ha: μ < 19
Recall that the test statistic, z, for a hypothesis is calculated as follows where x is the sample mean, μ0 is the hypothesized population mean, σ is the population standard deviation, and n is the sample size.
z = (x - μ0) / (σ / √n)
The value for μ0 is the hypothesized population mean we are testing for.
Here, we have μ0 = 19. The sample of 75 items gave a mean of 18.32, so we have n = 75 and x = 18.32. Finally, the standard deviation for all items was given to be 2, so we have σ = 2.
Text 2:
Step 1
(a) Compute the value of the test statistic.
A sample of 58 items provided a mean of x = 13 and a standard deviation of s = 6.7. The hypotheses are given below.
H0: μ = 14
Ha: μ ≠ 14
A t test statistic will be used when the standard deviation is calculated from a sample instead of the population. Recall that the test statistic, t, for a hypothesis is calculated as follows where x is the sample mean, μ0 is the hypothesized population mean, s is the population standard deviation, and n is the sample size.
t = (x - μ0) / (s / √n)
The value for μ0 is the hypothesized population mean we are testing for.
Here, we have μ0 = 14. There was a sample of 58 items given, so we have n = 58.
