A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 769 hours. A random sample of 22 light bulbs has a mean life of 743 hours. Assume the population is normally distributed and the population standard deviation is 56 hours. At α=0.05​, do you have enough evidence to reject the​ manufacturer's claim? Complete parts​ (a) through​ (e).       ​(a) Identify the null hypothesis and alternative hypothesis.     A. H0​: μ≥769 ​(claim) Ha​: μ<769   B. H0​: μ>769 Ha​: μ≤769 ​(claim)   C. H0​: μ≤743 Ha​: μ>743 ​(claim)   D. H0​: μ≠769​(claim) Ha​: μ=769   E. H0​: μ<743 ​(claim) Ha​: μ≥743   F. H0​: μ=743 Ha​: μ≠743 ​(claim) ​(b) Identify the critical​ value(s). Use technology.   z0=nothing ​(Use a comma to separate answers as needed. Round to two decimal places as​ needed.) ​(c) Identify the standardized test statistic. Use technology.   z=nothing ​(Round to two decimal places as​ needed.) ​(d) Decide whether to reject or fail to reject the null​ hypothesis, and​ (e) interpret the decision in the context of the original claim.     A. Reject H0. There is not sufficient evidence to reject the claim that mean bulb life is at least 769 hours.   B. Reject H0. There is sufficient evidence to reject the claim that mean bulb life is at least 769 hours.   C. Fail to reject H0. There is not sufficient evidence to reject the claim that mean bulb life is at least 769 hours.   D. Fail to reject H0. There is sufficient evidence to reject the claim that mean bulb life is at least 769 hours.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least
769
hours. A random sample of
22
light bulbs has a mean life of
743
hours. Assume the population is normally distributed and the population standard deviation is
56
hours. At
α=0.05​,
do you have enough evidence to reject the​ manufacturer's claim? Complete parts​ (a) through​ (e).
 
 
 
​(a) Identify the null hypothesis and alternative hypothesis.
 
 
A.
H0​:
μ≥769
​(claim)
Ha​:
μ<769
 
B.
H0​:
μ>769
Ha​:
μ≤769
​(claim)
 
C.
H0​:
μ≤743
Ha​:
μ>743
​(claim)
 
D.
H0​:
μ≠769​(claim)
Ha​:
μ=769
 
E.
H0​:
μ<743
​(claim)
Ha​:
μ≥743
 
F.
H0​:
μ=743
Ha​:
μ≠743
​(claim)
​(b) Identify the critical​ value(s). Use technology.
 
z0=nothing
​(Use a comma to separate answers as needed. Round to two decimal places as​ needed.)
​(c) Identify the standardized test statistic. Use technology.
 
z=nothing
​(Round to two decimal places as​ needed.)
​(d) Decide whether to reject or fail to reject the null​ hypothesis, and​ (e) interpret the decision in the context of the original claim.
 
 
A.
Reject
H0.
There
is not
sufficient evidence to reject the claim that mean bulb life is at least
769
hours.
 
B.
Reject
H0.
There
is
sufficient evidence to reject the claim that mean bulb life is at least
769
hours.
 
C.
Fail to reject
H0.
There
is not
sufficient evidence to reject the claim that mean bulb life is at least
769
hours.
 
D.
Fail to reject
H0.
There
is
sufficient evidence to reject the claim that mean bulb life is at least
769
hours.
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