Question
In: Statistics and Probability
Two catalysts in a batch chemical process, are being compared for their effect on the output...
Two catalysts in a batch chemical process, are being compared for their effect on the output of the process reaction. A sample of 12 batches was prepared using catalyst 1, and a sample of 10 batches was prepared using catalyst 2. The 12 batches for which catalyst 1 was used in the reaction gave an average yield of 85 with a sample standard deviation of 4, and the 10 batches for which catalyst 2 was used gave an average yield of 81 and a sample standard deviation of 5.
(1) Find a 90% confidence interval for the difference between the population means, assuming that the populations are approximately normally distributed with equal variances.
(2) Explain with the available sample information why the assumption of equal variances is reasonable.
Solutions
orchestra answered 1 year agoRelated Solutions
Two catalysts in a batch chemical process, are being compared for their effect on the output of the process reaction.
Two catalysts in a batch chemical process, are being compared for their effect on the output of the process reaction. A sample of 12 batches was prepared using catalyst 1, and a sample of 10 batches was prepared using catalyst 2. The 12 batches for which catalyst 1 was used in the reaction gave an average yield of 85 with a sample standard deviation of 4, and the 10 batches for which catalyst 2 was used gave an average yield...
Two catalysts in a batch chemical process, are being considered for their effect on the output...
Two catalysts in a batch chemical process, are being considered
for their effect on the output of a process reaction. Based on
literature, data with different samples with catalyst 1 were found
to result to the following yield:
78.53
78.17
81.05
81.77
78.13
81.24
81.84
79.63
78.59
79.74
79.84
On the other hand, you found the following for the yield using
catalyst 2:
82.05
81.57
81.71
81.29
81.79
81.47
81.75
81.50
81.75
If you can assume that the distribution characterizing...
Two catalysts are being considered for a chemical process. Sixteen batches were completed using Catalyst 1,...
Two catalysts are being considered for a chemical process.
Sixteen batches were completed using Catalyst 1, providing an
average yield of ?̅1 = 84 and a standard deviation of ?1 = 1.87.
Thirteen batches were run with Catalyst 2, and a mean yield of ?̅2
= 89 was found, along with ?2 = 1.48. Assume the underlying yield
data are Normally distributed.
(a) Is it believable that the variances of the two populations
differ? Use the appropriate hypothesis test with...
Two catalysts are being considered for a chemical process. Sixteen batches were completed using Catalyst 1,...
Two catalysts are being considered for a chemical process.
Sixteen batches were completed using Catalyst 1, providing an
average yield of ?̅1 = 84 and a standard deviation of ?1 = 1.87.
Thirteen batches were run with Catalyst 2, and a mean yield of ?̅2
= 89 was found, along with ?2 = 1.48. Assume the underlying yield
data are Normally distributed.
(a) Is it believable that the variances of the two populations
differ? Use the appropriate hypothesis test with...
Part C only: Two catalysts are being considered for a chemical process. Sixteen batches were completed...
Part C only:
Two catalysts are being considered for a chemical process.
Sixteen batches were completed using Catalyst 1, providing an
average yield of x1=84 and a standard
deviation of s1=1.87. Thirteen batches
were run with Catalyst 2, and a mean yield of
x2=89 was found, along with
s2=1.48. Assume the underlying yield
data are Normally distributed.
Is it believable that the variances of the two populations
differ? Use the appropriate hypothesis test with α = 0.05.
Based on your...
Two catalysts are being analyzed to determine how they affect the mean yield of a chemical...
Two catalysts are being analyzed to determine how they affect
the mean yield of a chemical process. Specifically, catalyst 1 is
currently in use, but catalyst 2 is acceptable. Since catalyst 2 is
cheaper, it should be adopted, providing it does not change the
process yield. An experiment is run in the pilot plant and results
in the data shown. (a) Is there any difference between the mean
yields? Use α = 0.05 and assume equal variances. (b) Find the...
Two catalysts are being analyzed to determine how they affect the mean yield of a chemical...
Two catalysts are being analyzed to determine how they affect
the mean yield of a chemical process. Specifically, catalyst 1 is
currently in use, but catalyst 2 is acceptable. Since catalyst 2 is
cheaper, it should be adopted, providing it does not change the
process yield. An experiment is run in the pilot plant and results
in the data shown.(a) Is there any difference between the mean
yields? Use α = 0.05 and assume equal variances. (b) Find the
100(1-α)...
Two catalysts are being analyzed to determine how they affect the mean yield of a chemical...
Two catalysts are being analyzed to determine how they affect
the mean yield of a chemical process. Specifically, catalyst 1 is
currently in use, but catalyst 2 is acceptable. Since catalyst 2 is
cheaper, it should be adopted, providing it does not change the
process yield. An experiment is run in the pilot plant and results
in the data shown. (a) Is there any difference between the mean
yields? Use α = 0.05 and assume equal variances. (b) Find the...
Two catalysts are being analyzed to determine how they affect the mean yield of a chemical...
Two catalysts are being analyzed to determine how they affect
the mean yield of a chemical process. Specifically, catalyst 1 is
currently used. Because catalyst 2 is cheaper, it should be
adopted, if it does not change the process yield. A test is run in
the pilot plant and results in the data shown in the Table below.
Both populations are assumed normal.
a) Assuming equal variances, using a hypothesis test at 5% alpha
level, show if there is any...
Two catalysts are being analyzed to determine how they affect the mean yield of a chemical...
Two catalysts are being analyzed to determine how they affect
the mean yield of a chemical process. Specifically, catalyst 1 is
currently used. Because catalyst 2 is cheaper, it should be
adopted, if it does not change the process yield. A test is run in
the pilot plant and results in the data shown in the Table below.
Both populations are assumed normal.
Observation #
Catalyst 1
Catalyst 1
1
91.5
89.19
2
94.18
90.95
3
92.18
90.46
4
95.39...
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