A simple random sample of size n=15 is drawn from a population that is normally distributed. The sample mean is found to

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A simple random sample of size n=15 is drawn from a
population that is normally distributed. The sample mean is found
to be x=32.5 and the sample standard deviation is found
to be s=6.3. Determine if the population mean is
different from 26 at the α=0.01 level of
significance. Complete parts ​(a) through ​(d) below.
Question content area bottom
Part 1
​(a) Determine the null and alternative hypotheses.
H0​:
pp
sigmaσ
muμ
▼
less than<
not equals≠
equals=
greater than>
26
H1​:
▼
sigmaσ
muμ
pp
▼
not equals≠
equals=
less than<
greater than>
26
Part 2
​(b) Calculate the​ P-value.
​P-value=enter your response here
​(Round to three decimal places as​ needed.)
Part 3
​(c) State the conclusion for the test.
A.
Do not reject
H0
because the​ P-value is
less than
the
α=0.01
level of significance.
B.
Reject
H0
because the​ P-value is
greater than
the
α=0.01
level of significance.
C.
Reject
H0
because the​ P-value is
less than
the
α=0.01
level of significance.
D.
Do not reject
H0
because the​ P-value is
greater than
the
α=0.01
level of significance.
Part 4
​(d) State the conclusion in context of the problem.
There
▼
is not
is
sufficient evidence at the
α=0.01
level of significance to conclude that the population mean is
different from