Question
A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 767 hours. A random sample of
A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least
767
hours. A random sample of
22
light bulbs has a mean life of
746
hours. Assume the population is normally distributed and the population standard deviation is
57
hours. At
?=0.08?,
do you have enough evidence to reject the? manufacturer's claim? Complete parts? (a) through? (e).
) Identify the null hypothesis and alternative hypothesis.
A.
H0?:
??746
Ha?:
?>746
?(claim)
B.
H0?:
?=746
Ha?:
??746
?(claim)
C.
H0?:
??767
?(claim)
Ha?:
?
D.
H0?:
?
?(claim)
Ha?:
??746
E.
H0?:
?>767
Ha?:
??767
?(claim)
F.
H0?:
??767?(claim)
Ha?:
?=767
Part 2?(b) Identify the critical? value(s). Use technology.
z0=enter your response here
?(Use a comma to separate answers as needed. Round to two decimal places as? needed.)Part 3Identify the rejection? region(s). Choose the correct answer below.
A.
-404z
RejectH0.
RejectH0.
FailtorejectH0.
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 1.4 and 1.4. The area under the curve to the left of negative 1.4 is shaded and the area under the curve to the right of 1.4 are both shaded one color and labeled Reject Upper H 0.The area under the curve between negative 1.4 and 1.4 is shaded another color and labeled Fail to reject Upper H 0.
B.
-404z
RejectH0.
FailtorejectH0.
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 1.4. The area under the curve to the right of 1.4 is shaded one color and labeled Reject Upper H 0. The area under the curve to the left of 1.4 is shaded another color and labeled Fail to reject Upper H 0.
C.
-404z
RejectH0.
FailtorejectH0.
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 1.4. The area under the curve to the left of negative 1.4 is shaded one color and labeled Reject Upper H 0. The area under the curve to the right of negative 1.4 is shaded another color and labeled Fail to reject Upper H 0.
Part 4?(c) Identify the standardized test statistic. Use technology.
z=enter your response here
?(Round to two decimal places as? needed.)Part 5?(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.
Failtoreject
H0.
There
is
sufficient evidence to reject the claim that mean bulb life is at least
767
hours.
B.
Reject
H0.
There
isnot
sufficient evidence to reject the claim that mean bulb life is at least
767
hours.
C.
Reject
H0.
There
is
sufficient evidence to reject the claim that mean bulb life is at least
767
hours.
D.
Failtoreject
H0.
There
isnot
sufficient evidence to reject the claim that mean bulb life is at least
767
hours.
) Identify the null hypothesis and alternative hypothesis.
A.
H0?:
??746
Ha?:
?>746
?(claim)
B.
H0?:
?=746
Ha?:
??746
?(claim)
C.
H0?:
??767
?(claim)
Ha?:
?
D.
H0?:
?
?(claim)
Ha?:
??746
E.
H0?:
?>767
Ha?:
??767
?(claim)
F.
H0?:
??767?(claim)
Ha?:
?=767
Part 2?(b) Identify the critical? value(s). Use technology.
z0=enter your response here
?(Use a comma to separate answers as needed. Round to two decimal places as? needed.)Part 3Identify the rejection? region(s). Choose the correct answer below.
A.
-404z
RejectH0.
RejectH0.
FailtorejectH0.
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 1.4 and 1.4. The area under the curve to the left of negative 1.4 is shaded and the area under the curve to the right of 1.4 are both shaded one color and labeled Reject Upper H 0.The area under the curve between negative 1.4 and 1.4 is shaded another color and labeled Fail to reject Upper H 0.
B.
-404z
RejectH0.
FailtorejectH0.
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 1.4. The area under the curve to the right of 1.4 is shaded one color and labeled Reject Upper H 0. The area under the curve to the left of 1.4 is shaded another color and labeled Fail to reject Upper H 0.
C.
-404z
RejectH0.
FailtorejectH0.
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 1.4. The area under the curve to the left of negative 1.4 is shaded one color and labeled Reject Upper H 0. The area under the curve to the right of negative 1.4 is shaded another color and labeled Fail to reject Upper H 0.
Part 4?(c) Identify the standardized test statistic. Use technology.
z=enter your response here
?(Round to two decimal places as? needed.)Part 5?(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.
Failtoreject
H0.
There
is
sufficient evidence to reject the claim that mean bulb life is at least
767
hours.
B.
Reject
H0.
There
isnot
sufficient evidence to reject the claim that mean bulb life is at least
767
hours.
C.
Reject
H0.
There
is
sufficient evidence to reject the claim that mean bulb life is at least
767
hours.
D.
Failtoreject
H0.
There
isnot
sufficient evidence to reject the claim that mean bulb life is at least
767
hours.
?(a) Identify the null hypothesis and alternative hypothesis.
A.
H0?:
??746
Ha?:
?>746
?(claim)
B.
H0?:
?=746
Ha?:
??746
?(claim)
C.
H0?:
??767
?(claim)
Ha?:
?
D.
H0?:
?
?(claim)
Ha?:
??746
E.
H0?:
?>767
Ha?:
??767
?(claim)
F.
H0?:
??767?(claim)
Ha?:
?=767
Part 2?(b) Identify the critical? value(s). Use technology.
z0=enter your response here
?(Use a comma to separate answers as needed. Round to two decimal places as? needed.)Part 3Identify the rejection? region(s). Choose the correct answer below.
A.
-404z
RejectH0.
RejectH0.
FailtorejectH0.
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 1.4 and 1.4. The area under the curve to the left of negative 1.4 is shaded and the area under the curve to the right of 1.4 are both shaded one color and labeled Reject Upper H 0.The area under the curve between negative 1.4 and 1.4 is shaded another color and labeled Fail to reject Upper H 0.
B.
-404z
RejectH0.
FailtorejectH0.
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 1.4. The area under the curve to the right of 1.4 is shaded one color and labeled Reject Upper H 0. The area under the curve to the left of 1.4 is shaded another color and labeled Fail to reject Upper H 0.
C.
-404z
RejectH0.
FailtorejectH0.
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 1.4. The area under the curve to the left of negative 1.4 is shaded one color and labeled Reject Upper H 0. The area under the curve to the right of negative 1.4 is shaded another color and labeled Fail to reject Upper H 0.
Part 4?(c) Identify the standardized test statistic. Use technology.
z=enter your response here
?(Round to two decimal places as? needed.)Part 5?(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.
Failtoreject
H0.
There
is
sufficient evidence to reject the claim that mean bulb life is at least
767
hours.
B.
Reject
H0.
There
isnot
sufficient evidence to reject the claim that mean bulb life is at least
767
hours.
C.
Reject
H0.
There
is
sufficient evidence to reject the claim that mean bulb life is at least
767
hours.
D.
Failtoreject
H0.
There
isnot
sufficient evidence to reject the claim that mean bulb life is at least
767
hours.
?(a) Identify the null hypothesis and alternative hypothesis.
A.
H0?:
??746
Ha?:
?>746
?(claim)
B.
H0?:
?=746
Ha?:
??746
?(claim)
C.
H0?:
??767
?(claim)
Ha?:
?
D.
H0?:
?
?(claim)
Ha?:
??746
E.
H0?:
?>767
Ha?:
??767
?(claim)
F.
H0?:
??767?(claim)
Ha?:
?=767
Part 2?(b) Identify the critical? value(s). Use technology.
z0=enter your response here
?(Use a comma to separate answers as needed. Round to two decimal places as? needed.)Part 3Identify the rejection? region(s). Choose the correct answer below.
A.
-404z
RejectH0.
RejectH0.
FailtorejectH0.
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 1.4 and 1.4. The area under the curve to the left of negative 1.4 is shaded and the area under the curve to the right of 1.4 are both shaded one color and labeled Reject Upper H 0.The area under the curve between negative 1.4 and 1.4 is shaded another color and labeled Fail to reject Upper H 0.
B.
-404z
RejectH0.
FailtorejectH0.
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 1.4. The area under the curve to the right of 1.4 is shaded one color and labeled Reject Upper H 0. The area under the curve to the left of 1.4 is shaded another color and labeled Fail to reject Upper H 0.
C.
-404z
RejectH0.
FailtorejectH0.
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 1.4. The area under the curve to the left of negative 1.4 is shaded one color and labeled Reject Upper H 0. The area under the curve to the right of negative 1.4 is shaded another color and labeled Fail to reject Upper H 0.
Part 4?(c) Identify the standardized test statistic. Use technology.
z=enter your response here
?(Round to two decimal places as? needed.)Part 5?(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.
Failtoreject
H0.
There
is
sufficient evidence to reject the claim that mean bulb life is at least
767
hours.
B.
Reject
H0.
There
isnot
sufficient evidence to reject the claim that mean bulb life is at least
767
hours.
C.
Reject
H0.
There
is
sufficient evidence to reject the claim that mean bulb life is at least
767
hours.
D.
Failtoreject
H0.
There
isnot
sufficient evidence to reject the claim that mean bulb life is at least
767
hours.
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Stochastic Calculus With Infinitesimals
Authors: Frederik S Herzberg
1st Edition
3642331491, 9783642331497
