Use technology and a​ t-test to test the claim about the population mean μ at the given level of significance α using the given sample statistics. Assume the population is normally distributed.   ​Claim: μ>78​;

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Use technology and a​ t-test to test the claim about the population mean
μ
at the given level of significance
α
using the given sample statistics. Assume the population is normally distributed.
 
​Claim:
μ>78​;
α=0.01    
Sample​ statistics:
x=80.7​,
s=3.4​,
n=26
What are the null and alternative​ hypotheses? Choose the correct answer below.
 
 
A.
H0​:
μ≤78
HA​:
μ>78
 
B.
H0​:
μ≥78
HA​:
μ<78
 
C.
H0​:
μ≠78
HA​:
μ=78
 
D.
H0​:
μ=78
HA​:
μ≠78
What is the value of the standardized test​ statistic?
 
The standardized test statistic is
nothing.
​(Round to two decimal places as​ needed.)
What is the​ P-value of the test​ statistic?
 
​P-value=nothing
​(Round to three decimal places as​ needed.)
Decide whether to reject or fail to reject the null hypothesis. Choose the correct answer below.
 
 
A.
Reject
H0.
There
is
enough evidence to support the claim.
 
B.
Reject
H0.
There
is not
enough evidence to support the claim.
 
C.
Fail to reject
H0.
There
is
enough evidence to support the claim.
 
D.
Fail to reject
H0.
There
is not
enough evidence to support the claim.
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