Consider the following hypotheses:
H_{0}: μ ≤ 30.4
H_{A}: μ > 30.4
A sample of 55 observations yields a sample mean of 31.9. Assume
that the sample is drawn from a normal population with a population
standard deviation of 5.2. (You may find it useful to
reference the appropriate table: z table
or t table)
a-1. Find the p-value.
p-value < 0.01
a-2. What is the conclusion if α =
0.01?
Reject H_{0} since the p-value is greater than α.
Reject H_{0} since the p-value is smaller than α.
Do not reject H_{0} since the p-value is greater than α.
Do not reject H_{0} since the p-value is smaller than α.
a-3. Interpret the results at α =
0.01.
We conclude that the sample mean is greater than 30.4.
We cannot conclude that the sample mean is greater than 30.4.
We conclude that the population mean is greater than 30.4.
We cannot conclude that the population mean is greater than 30.4.
b-1. Calculate the p-value if the above
sample mean was based on a sample of 120 observations.
p-value < 0.01
b-2. What is the conclusion if α =
0.01?
Reject H_{0} since the p-value is smaller than α.
Reject H_{0} since the p-value is greater than α.
Do not reject H_{0} since the p-value is smaller than α.
Do not reject H_{0} since the p-value is greater than α.
b-3. Interpret the results at α =
0.01.
We conclude that the sample mean is greater than 30.4.
We cannot conclude that the sample mean is greater than 30.4.
We conclude that the population mean is greater than 30.4.
We cannot conclude that the population mean is greater than 30.4.
a-1)
0.01 p-value < 0.025
a-2)
Do not reject H_{0} since the p-value is greater than α.
a-3)
We cannot conclude that the population mean is greater than 30.4.
b-1)p-value < 0.01
b-2)Reject H_{0} since the p-value is smaller than α.
b-3)
We conclude that the population mean is greater than 30.4.
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