The following information is available.
H0 : μ ≥ 220
H1 : μ < 220
A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the .025 significance level.
a.
Is this a one- or two-tailed test?
One-tailed test
b.
What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)
H0 when z < -2.00
c.
What is the value of the test statistic? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
Value of the test statistic= ? I cannot not calculate this one I think it is 2.667, but it is wrong
d.
What is your decision regarding H0?
Reject
e.
What is the p-value? (Round your answer to 4 decimal places.)
p-value=.0038
To answer part c, we need to calculate the value of the test statistic. The test statistic for a one-sample z-test is calculated using the formula:
z = (sample mean - population mean) / (population standard deviation / sqrt(sample size))
Given the following information:
Sample mean (x̄) = 215
Population mean (μ) = 220
Population standard deviation (σ) = 15
Sample size (n) = 64
We can plug these values into the formula and calculate the test statistic:
z = (215 - 220) / (15 / sqrt(64))
z = -5 / (15 / 8)
z = -5 * (8/15)
z = -2.67 (rounded to 2 decimal places)
Therefore, the value of the test statistic is -2.67.