Question
In: Statistics and Probability
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 α = 0.05.
(b) Based on your answer to part (a), calculate the appropriate 99% CI to test if the mean yields for the two catalysts differ. Give your conclusions with context.
(c) If 4 batches made with Catalyst 1 were found to be below the yield specification, and 3 batches made using Catalyst 2 were below specification, calculate the 95% CI to determine if the proportion of batches that fall under specification is the same for the two Catalysts.
Solutions
orchestra answered 2 years agoRelated Solutions
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 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 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...
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...
1. To study the effect of temperature on yield in a chemical process, five batches were...
1. To study the effect of temperature on yield in a chemical
process, five batches were produced at each of three temperature
levels. The results follow. Temperature 50°C 60°C 70°C 31 30 24 21
31 29 33 34 29 36 23 31 29 27 32 a. Construct an analysis of
variance table (to 2 decimals but p-value to 4 decimals, if
necessary).
Source of Variation Sum of Squares Degrees of Freedom Mean
Square F p-value Treatments 2 0.0 Error 12...
Yield of Chemical Process Two catalysts were analyzed to determine how they affect the mean yield...
Yield of Chemical Process Two catalysts were
analyzed to determine how they affect the mean yield of chemical
process. Specifically, catalyst 1 is currently used; but catalyst 2
is acceptable. Because catalyst 2 is cheaper, it should be adopted,
if it does not change the process yield. Two tests were run in the
pilot plant. Eight samples of each type of catalyst were randomly
and independently selected from the pilot plant, and the chemical
process yield were recorded. The data...
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...
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