1.) Consider the following hypothesis test. H0: 𝜇 = 100 Ha: 𝜇 ≠ 100 A sample of 65 is used. Identify the

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1.)
Consider the following hypothesis test.
H0: 𝜇 = 100
Ha: 𝜇 ≠ 100
A sample of 65 is used. Identify the p-value and
state your conclusion for each of the following sample results.
Use
𝛼 = 0.05.
(a)
x = 104 and s = 11.6
Find the value of the test statistic. (Round your answer to
three decimal places.)
Find the p-value. (Round your answer to four
decimal places.)
p-value =
State your conclusion.
Do not reject H0. There is insufficient
evidence to conclude that 𝜇 ≠ 100.
Reject H0. There is sufficient evidence to
conclude
that 𝜇 ≠ 100. Reject H0.
There is insufficient evidence to conclude
that 𝜇 ≠ 100. Do not
reject H0. There is sufficient evidence to
conclude that 𝜇 ≠ 100.
(b)
x = 96.5 and s = 11.0
Find the value of the test statistic. (Round your answer to
three decimal places.)
Find the p-value. (Round your answer to four
decimal places.)
p-value =
State your conclusion.
Do not reject H0. There is insufficient
evidence to conclude
that 𝜇 ≠ 100.Reject H0.
There is sufficient evidence to conclude
that 𝜇 ≠ 100. Reject H0.
There is insufficient evidence to conclude
that 𝜇 ≠ 100.Do not
reject H0. There is sufficient evidence to
conclude that 𝜇 ≠ 100.
(c)
x = 102 and s = 10.6
Find the value of the test statistic. (Round your answer to
three decimal places.)
Find the p-value. (Round your answer to four
decimal places.)
p-value =
State your conclusion.
Do not reject H0. There is insufficient
evidence to conclude that 𝜇 ≠ 100.
Reject H0. There is sufficient evidence to
conclude
that 𝜇 ≠ 100. Reject H0.
There is insufficient evidence to conclude
that 𝜇 ≠ 100. Do not
reject H0. There is sufficient evidence to
conclude that 𝜇 ≠ 100.
2.)
Consider the following hypothesis test.
A sample of 40 provided a sample mean of 26.8. The
population standard deviation is 6.
(a)
Find the value of the test statistic. (Round your answer to two
decimal places.)
(b)
Find the p-value. (Round your answer to four
decimal places.)
p-value =
(c)
At
𝛼 = 0.01,
state your conclusion.
Reject H0. There is sufficient evidence
to conclude that 𝜇 > 25.
Reject H0. There is insufficient evidence
to conclude that 𝜇 >
25. Do not
reject H0. There is sufficient evidence to
conclude that 𝜇 > 25. Do not
reject H0. There is insufficient evidence
to conclude that 𝜇 > 25.
(d)
State the critical values for the rejection rule. (Round your
answer to two decimal places. If the test is one-tailed, enter NONE
for the unused tail.)
test statistic≤test statistic≥
State your conclusion.
Reject H0. There is sufficient evidence
to conclude that 𝜇 > 25.
Reject H0. There is insufficient evidence
to conclude that 𝜇 >
25. Do not
reject H0. There is sufficient evidence to
conclude that 𝜇 > 25. Do not
reject H0. There is insufficient evidence
to conclude that 𝜇 > 25.