# A light bulb manufacturer guar

A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least

761

hours. A random sample of

30

light bulbs has a mean life of

739

hours. Assume the population is normally distributed and the population standard deviation is

59

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=739
Ha​:
μ≠739

​(claim)

B.

H0​:
μ≠761​(claim)
Ha​:
μ=761

C.

H0​:
μ≤739
Ha​:
μ>739

​(claim)

D.

H0​:
μ<739

​(claim)

Ha​:
μ≥739

E.

H0​:
μ>761
Ha​:
μ≤761

​(claim)

F.

H0​:
μ≥761

​(claim)

Ha​:
μ<

# A light bulb manufacturer guar

A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 736 hours. A random sample of 21 light bulbs has a mean life of 723 hours. Assume the population is normally distributed and the population standard deviation is 63 hours. At α=0.08​, do you have enough evidence to reject the​ manufacturer’s claim? Complete parts​ (a) through​ (e)

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

identify the rejection​ region(s). Choose the correct answer below.

Identify the standardized test statistic. Use technology.

​(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 light bulb manufacturer guar

A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least

744

hours. A random sample of

30

light bulbs has a mean life of

732

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≥744

​(claim)

Ha​:
μ<744

B.

H0​:
μ≠744​(claim)
Ha​:
μ=744

C.

H0​:
μ=732
Ha​:
μ≠732

​(claim)

D.

H0​:
μ<732

​(claim)

Ha​:
μ≥732

E.

H0​:
μ≤732
Ha​:
μ>732

​(claim)

F.

H0​:
μ>744
Ha​:
μ≤744

​(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.)
Identify the rejection​ region(s). Choose the correct answer below.

A.

-404z

Reject H0.
Fail to reject H0.

•
•
•

A normal curve is over a horizontal z-axis labeled from negative 4 to 4 in increments of 1 and is centered on 0. A vertical line segment extends from the horizontal axis to the curve at negative 2.1. The area under the curve to the left of negative 2.1 is shaded one color and labeled Reject Upper H 0. The area under the curve to the right of negative 2.1 is shaded another color and labeled Fail to reject Upper H 0.

B.

-404z

Reject H0.
Reject H0.
Fail to reject H0.

•
•
•

A normal curve is over a horizontal z-axis labeled from negative 4 to 4 in increments of 1 and is centered on 0. Vertical line segments extend from the horizontal axis to the curve at negative 2.1 and 2.1. The area under the curve to the left of negative 2.1 is shaded and the area under the curve to the right of 2.1 are both shaded one color and labeled Reject Upper H 0.The area under the curve between negative 2.1 and 2.1 is shaded another color and labeled Fail to reject Upper H 0.

C.

-404z

Reject H0.
Fail to reject H0.

•
•
•

A normal curve is over a horizontal z-axis labeled from negative 4 to 4 in increments of 1 and is centered on 0. A vertical line segment extends from the horizontal axis to the curve at 2.1. The area under the curve to the right of 2.1 is shaded one color and labeled Reject Upper H 0. The area under the curve to the left of 2.1 is shaded another color and labeled Fail to reject Upper H 0.

​(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

744

hours.

B.

Fail to reject
H0.

There

is

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

744

hours.

C.

Reject
H0.

There

is

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

744

hours.

D.

Fail to reject
H0.

There

is not

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

744

hours.

# A light bulb manufacturer guar

A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 766 hours. A random sample of 30 light bulbs has a mean life of 754 hours. Assume the population is normally distributed and the population standard deviation is 61 hours. At α=0.08​, do you have enough evidence to reject the​ manufacturer’s claim? Complete parts​ (a) through​ (e).

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

Identify the standardized test statistic. Use technology.

​(d) Decide whether to reject or fail to reject the null​ hypothesis, and​(e) interpret the decision in the context of the original claim.

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