9-12 Consider the following hypotheses:
H_{0}: μ = 33
H_{A}: μ ≠ 33
The population is normally distributed. A sample produces the
following observations: (You may find it useful to
reference the appropriate table: z table
or t table)
38 | 31 | 34 | 36 | 33 | 38 | 28 |
a. Find the mean and the standard deviation.
(Round your answers to 2 decimal
places.)
b. Calculate the value of the test statistic.
(Round intermediate calculations to at least 4 decimal
places and final answer to 2 decimal places.)
c. Find the p-value.
p-value < 0.01
d. At the 5% significance level, what is the
conclusion?
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.
e. Interpret the results αα =
0.05.
We conclude that the sample mean differs from 33.
We cannot conclude that the population mean differs from 33.
We conclude that the population mean differs from 33.
We cannot conclude that the sample mean differs from 33.
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