9. Prof J is investigating the amount of heat necessary to melt ice to water using two different designs. One design used an electric heater and the other design involved mixing ice with aluminium. A random sample of 26 measurements using electric heater produced a variance of 1128.96kj/kg and a random sample of 10 measurements using mixing ice with aluminium produced a variance of 1600kJ /kg. (a) Assuming that the samples above come from a normal population with variance o?, construct a 95% c.i of the standard deviation of the amount of heat necessary to melt ice to water using electric heater. (b) Construct a 95% c.i for the ratio of variances for the amount of heat between the two different designs above. State any further assumptions you make. (c) Based on the results obtained in (b), do you have reasons to believe the variance of heat measurement for both designs are equal?
9. Prof J is investigating the amount of heat necessary to melt ice to water using two different designs. One design used an electric heater and the other design involved mixing ice with aluminium. A random sample of 26 measurements using electric heater produced a variance of 1128.96kj/kg and a random sample of 10 measurements using mixing ice with aluminium produced a variance of 1600kJ /kg. (a) Assuming that the samples above come from a normal population with variance o?, construct a 95% c.i of the standard deviation of the amount of heat necessary to melt ice to water using electric heater. (b) Construct a 95% c.i for the ratio of variances for the amount of heat between the two different designs above. State any further assumptions you make. (c) Based on the results obtained in (b), do you have reasons to believe the variance of heat measurement for both designs are equal?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
Related questions
Question
![9. Prof J is investigating the amount of heat necessary to melt ice to water using two different
designs. One design used an electric heater and the other design involved mixing ice with
aluminium. A random sample of 26 measurements using electric heater produced a variance of
1128.96kj /kg and a random sample of 10 measurements using mixing ice with aluminium
produced a variance of 1600ks /kg.
(a) Assuming that the samples above come from a normal population with variance o?, construct a
95% c.i of the standard deviation of the amount of heat necessary to melt ice to water using
electric heater.
(b) Construct a 95% c.i for the ratio of variances for the amount of heat between the two different
designs above. State any further assumptions you make.
(c) Based on the results obtained in (b), do you have reasons to believe the variance of heat
measurement for both designs are equal?
ref:FS20607]
10. The diameter (in millimeters) of steel rods manufactured on two different extrusion machines is
being investigated. Two random samples are selected. The sample mean and sample standard
deviation for the first sample of size 10 are given by 90 and 5 respectively. The sample mean and
sample standard deviation for the second sample of size 15 are given by 87 and 4 respectively.
Assume that the population variances for the diameters from both extrusion machines are equal
and that the data are drawn from a normal population.
(a) Construct a 95% confidence interval for the difference in mean rod diameter.[(-0.72, 6.72)]
From the interval constructed in (a), do you agree that there is a difference in mean rod
diameter of steel rods from the two machines? Justify.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc7dafc2c-dbbb-4387-b179-47866e583f7d%2F4b7bdbac-9abe-4ef1-a357-49f40bad547d%2Ftiwbsbt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:9. Prof J is investigating the amount of heat necessary to melt ice to water using two different
designs. One design used an electric heater and the other design involved mixing ice with
aluminium. A random sample of 26 measurements using electric heater produced a variance of
1128.96kj /kg and a random sample of 10 measurements using mixing ice with aluminium
produced a variance of 1600ks /kg.
(a) Assuming that the samples above come from a normal population with variance o?, construct a
95% c.i of the standard deviation of the amount of heat necessary to melt ice to water using
electric heater.
(b) Construct a 95% c.i for the ratio of variances for the amount of heat between the two different
designs above. State any further assumptions you make.
(c) Based on the results obtained in (b), do you have reasons to believe the variance of heat
measurement for both designs are equal?
ref:FS20607]
10. The diameter (in millimeters) of steel rods manufactured on two different extrusion machines is
being investigated. Two random samples are selected. The sample mean and sample standard
deviation for the first sample of size 10 are given by 90 and 5 respectively. The sample mean and
sample standard deviation for the second sample of size 15 are given by 87 and 4 respectively.
Assume that the population variances for the diameters from both extrusion machines are equal
and that the data are drawn from a normal population.
(a) Construct a 95% confidence interval for the difference in mean rod diameter.[(-0.72, 6.72)]
From the interval constructed in (a), do you agree that there is a difference in mean rod
diameter of steel rods from the two machines? Justify.
![(a) It is given that the 95% c.i for the mean lifespan of Energy lightbulbs is (1023.3 hour, 1101.7
hour). This interval is based on results from a random sample of 121 light bulbs. Hence, find the
99% c.i for the mean lifespan of this brand of light bulbs. [(1010.984, 1114.016)]
(b) A manufacturer wants to assess the percentage of defective output in a large batch produced
by a cutting machine. A random sample of 300 output was tested and found that 45 of them were
defective. Calculate a 98% c.i for the percentage of defective output in the complete batch.
[(0.102,0.198)]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc7dafc2c-dbbb-4387-b179-47866e583f7d%2F4b7bdbac-9abe-4ef1-a357-49f40bad547d%2Ft5e984j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) It is given that the 95% c.i for the mean lifespan of Energy lightbulbs is (1023.3 hour, 1101.7
hour). This interval is based on results from a random sample of 121 light bulbs. Hence, find the
99% c.i for the mean lifespan of this brand of light bulbs. [(1010.984, 1114.016)]
(b) A manufacturer wants to assess the percentage of defective output in a large batch produced
by a cutting machine. A random sample of 300 output was tested and found that 45 of them were
defective. Calculate a 98% c.i for the percentage of defective output in the complete batch.
[(0.102,0.198)]
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