Question

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

753

hours. A random sample of

20

light bulbs has a mean life of

732

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

61

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<732

​(claim)

Ha​:

μ≥732

B.

H0​:

μ≠753​(claim)

Ha​:

μ=753

C.

H0​:

μ=732

Ha​:

μ≠732

​(claim)

D.

H0​:

μ≤732

Ha​:

μ>732

​(claim)

E.

H0​:

μ>753

Ha​:

μ≤753

​(claim)

F.

H0​:

μ≥753

​(claim)

Ha​:

μ<753

​(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.

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.

B.-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.-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.

​(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

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

753

hours.

B.

Fail to reject

H0.

There

is

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

753

hours.

C.

Reject

H0.

There

is not

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

753

hours.

D.

Fail to reject

H0.

There

is not

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

753

hours.

Answer 1

uhoni- a Ho: els 753 th Hall2 753 bro La = -2.05 N Rejection Meer region reject Ho, it Z 2 - 2.05 2 X-M olm 732-753 61/izo -1.54 راه Fail to reject Ho. There is not sufficient to reject the claim. evidence