Consider the following hypotheses:
H_{0}: μ ≤ 12.6
H_{A}: μ > 12.6
A sample of 25 observations yields a sample mean of 13.4. Assume
that the sample is drawn from a normal population with a population
standard deviation of 3.2. (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
0.01 ≤ p-value < 0.025
0.025 ≤ p-value < 0.05
0.05 ≤ p-value < 0.10
p-value ≥ 0.10
a-2. What is the conclusion if α =
0.10?
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 =
0.10.
We conclude that the sample mean is greater than 12.6.
We cannot conclude that the sample mean is greater than 12.6.
We conclude that the population mean is greater than 12.6.
We cannot conclude that the population mean is greater than 12.6.
b-1. Calculate the p-value if the above
sample mean was based on a sample of 100 observations.
p-value < 0.01
0.01 ≤ p-value < 0.025
0.025 ≤ p-value < 0.05
0.05 ≤ p-value < 0.10
p-value ≥ 0.10
b-2. What is the conclusion if α =
0.10?
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.
b-3. Interpret the results at α =
0.10.
We conclude that the sample mean is greater than 12.6.
We cannot conclude that the sample mean is greater than 12.6.
We conclude that the population mean is greater than 12.6.
We cannot conclude that the population mean is greater than 12.6.
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