Question

1. Four catalysts that may affect the concentration of one component in a three- component liquid mixture are being investigated. The following concentrations are obtained from a completely randomized experiment: Catalyst Observations ($y_{ij}$) 1 2 3 4 1 58.2 56.3 50.1 52.9 2 57.2 54.5 54.2 49.9 3 58.4 57.0 m 50.0 4 55.8 55.3 51.7 5 55.2 Total 284.8 223.1 104.3+m 204.5 Assume that the data are normally distributed, $y_{ij} \sim N(\mu_i, \sigma^2)$, i = 1,2,3,4 and $1 \leq j \leq 5$. a) Write a full linear model for this experiment and explain the terms. b) Based on the model in part (a), obtain a formula for the residual for the observation in the position m. Hence, estimate of m which make the corresponding residual zero. c) Analyze the data and draw conclusions. Use $\alpha = 0.05$. d) Test all pairs of means using the Fisher Least Significant Difference (LSD) method with $\alpha = 0.05$. Comment on your findings. e) Describe briefly how to check the model assumptions.

          1. Four catalysts that may affect the concentration of one component in a three-
component liquid mixture are being investigated. The following concentrations are
obtained from a completely randomized experiment:
Catalyst
Observations ($y_{ij}$)
1
2
3
4
1
58.2
56.3
50.1
52.9
2
57.2
54.5
54.2
49.9
3
58.4
57.0
m
50.0
4
55.8
55.3
51.7
5
55.2
Total
284.8
223.1
104.3+m
204.5
Assume that the data are normally distributed, $y_{ij} \sim N(\mu_i, \sigma^2)$, i = 1,2,3,4 and
$1 \leq j \leq 5$.
a) Write a full linear model for this experiment and explain the terms.
b) Based on the model in part (a), obtain a formula for the residual for the
observation in the position m. Hence, estimate of m which make the
corresponding residual zero.
c) Analyze the data and draw conclusions. Use $\alpha = 0.05$.
d) Test all pairs of means using the Fisher Least Significant Difference (LSD)
method with $\alpha = 0.05$. Comment on your findings.
e) Describe briefly how to check the model assumptions.

1. Four catalysts that may affect the concentration of one component in a three-
component liquid mixture are being investigated. The following concentrations are
obtained from a completely randomized experiment:
Catalyst
Observations (yij)
1
2
3
4
1
58.2
56.3
50.1
52.9
2
57.2
54.5
54.2
49.9
3
58.4
57.0
m
50.0
4
55.8
55.3
51.7
5
55.2
Total
284.8
223.1
104.3+m
204.5
Assume that the data are normally distributed, yij∼ N(, σ^2), i = 1,2,3,4 and
1 ≤ j ≤ 5.
a) Write a full linear model for this experiment and explain the terms.
b) Based on the model in part (a), obtain a formula for the residual for the
observation in the position m. Hence, estimate of m which make the
corresponding residual zero.
c) Analyze the data and draw conclusions. Use α = 0.05.
d) Test all pairs of means using the Fisher Least Significant Difference (LSD)
method with α = 0.05. Comment on your findings.
e) Describe briefly how to check the model assumptions.

Added by Nancy R.

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