A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 738hours. A random sample of 26 light bulbs has a mean life of 711 hours. Assume the population is...


A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 738hours. A random sample of 26
light bulbs has a mean life of 711 hours. Assume the population is normally distributed and the population standard deviation is 55 hours. At α=0.02​,
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≠738​(claim)



Ha​:

μ=738







B.



H0​:

μ≤711



Ha​:

μ>711

​(claim)






C.



H0​:

μ=711



Ha​:

μ≠711

​(claim)






D.



H0​:

μ<>

​(claim)


Ha​:

μ≥711







E.



H0​:

μ≥738

​(claim)


Ha​:

μ<>







F.



H0​:

μ>738



Ha​:

μ≤738

​(claim)







​(b) Identify the critical​ value(s). Use technology.



z0=________________________________________


​(Use a comma to separate answers as needed. Round to two decimal places as​ needed.)



Identify the rejection​ region(s).


PICTURE ATTACHED


Choose the correct answer below.



​(c) Identify the standardized test statistic. Use technology.



z=_____________________________________________

​(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

sufficient evidence to reject the claim that mean bulb life is at least
738

hours.






B.



Fail to reject

H0.

There
is not

sufficient evidence to reject the claim that mean bulb life is at least
738

hours.






C.



Fail to reject

H0.

There
is

sufficient evidence to reject the claim that mean bulb life is at least
738

hours.






D.



Reject

H0.

There
is not

sufficient evidence to reject the claim that mean bulb life is at least
738

hours.



















Alight bub manufacturer guarantees thatr the mean ife of a certain type of light bub is at least 738 hours Arandom sample of 26 ight buibs has a mean ife of 711 hours. Assume the population is nomaly distributed and the population<br>standard deviation is 55 hours At a=002, do you have enough evidence to reject the manufacturer's dam? Compiete parts (a) trough (e)<br>(Use a comma to separate answers as needed. Round to two decimal places as needed)<br>Identty the rejection regons) Choose the conect answer below<br>OA<br>OB.<br>Fal<br>Faltereject<br>Falr H<br>Ret<br>Reject H<br>Rject<br>Reje<br>) ldentify the standardized test statistie Use technology<br>2- Round to beo decimal places as needed)<br>(4) Decide whether to reject or tail to reject the nul hypothesis, and (e) interpret the decision in the context of the original claim<br>Click to select your answerts)<br>

Extracted text: Alight bub manufacturer guarantees thatr the mean ife of a certain type of light bub is at least 738 hours Arandom sample of 26 ight buibs has a mean ife of 711 hours. Assume the population is nomaly distributed and the population standard deviation is 55 hours At a=002, do you have enough evidence to reject the manufacturer's dam? Compiete parts (a) trough (e) (Use a comma to separate answers as needed. Round to two decimal places as needed) Identty the rejection regons) Choose the conect answer below OA OB. Fal Faltereject Falr H Ret Reject H Rject Reje ) ldentify the standardized test statistie Use technology 2- Round to beo decimal places as needed) (4) Decide whether to reject or tail to reject the nul hypothesis, and (e) interpret the decision in the context of the original claim Click to select your answerts)
Jun 08, 2022
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