Question
In: Statistics and Probability
To study the effect of temperature on yield in a chemical process, five batches were produced...
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 | ||
| 30 | 26 | 24 | ||
| 20 | 27 | 29 | ||
| 32 | 30 | 29 | ||
| 35 | 19 | 31 | ||
| 28 | 23 | 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 | |||||
| Error | |||||
| Total |
b. Use a .05 level of significance to test whether the temperature level has an effect on the mean yield of the process.
Calculate the value of the test statistic (to 2 decimals).
The -value is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 12
What is your conclusion?
Solutions
Expert Solution
Solution:
We can use the excel ANOVA: Single Factor data analysis
tool to find the answer to the given questions.
The excel steps are:
Enter the data in excel.
Click on Data > Data Analysis > ANOVA: Single Factor > OK
Input Range: Select the data range for all the data including labels
Mark Labels in the first row
Alpha = 0.05
Choose the output range and click OK.
The output is given below:
| Anova: Single Factor | ||||||
| SUMMARY | ||||||
| Groups | Count | Sum | Average | Variance | ||
| 50°C | 5 | 145 | 29 | 32 | ||
| 60°C | 5 | 125 | 25 | 17.5 | ||
| 70°C | 5 | 145 | 29 | 9.5 | ||
| ANOVA | ||||||
| Source of Variation | SS | df | MS | F | P-value | F crit |
| Between Groups | 53.33333333 | 2 | 26.66666667 | 1.355932203 | 0.294497217 | 3.885293835 |
| Within Groups | 236 | 12 | 19.66666667 | |||
| Total | 289.3333333 | 14 |
a. Construct an analysis of variance table (to 2 decimals but p-value to 4 decimals, if necessary).
Answer:
| Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F | p-value |
| Treatments | 53.33 | 2 | 26.67 | 1.36 | 0.2945 |
| Error | 236 | 12 | 19.67 | ||
| Total | 289.33 | 14 |
b. Use a .05 level of significance to test whether the temperature level has an effect on the mean yield of the process.
Calculate the value of the test statistic (to 2 decimals).
Answer: The value of the test statistic is:
The p-value is greater than .10
What is your conclusion?
Since the p-value is greater than the significance level, we, therefore, fail to reject the null hypothesis and conclude that the temperature level has no significant effect on the mean yield of the process.
orchestra answered 2 years agoRelated Solutions
To study the effect of temperature on yield in a chemical process, five batches were produced...
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
37
35
30
27
36
35
39
39
35
42
28
37
35
32
38
A. Construct an analysis of variance table (to 2 decimals, if
necessary). Round p-value to four decimal places.
Source of variation
sum of squares
degrees of freedom
mean square
F
P- Value
Treatments
Error
Total...
To study the effect of temperature on yield in a chemical process, five batches were produced...
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
32
34
29
22
35
34
34
38
34
37
27
36
30
31
37
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
Error
Total
b. Use a level...
To study the effect of temperature on yield in a chemical process, five batches were produced...
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
32
30
25
22
31
30
34
34
30
37
23
32
30
27
33
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
Error
Total
b. Use a.05...
To study the effect of temperature on yield in a chemical process, five batches were produced...
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
33
23
21
34
28
33
37
28
36
26
30
29
30
31
a. Construct an analysis of variance table (to 2 decimals but
p-value to 4 decimals, if necessary).
b. Use a level of significance to test whether the temperature
level has an effect on the mean yield...
To study the effect of temperature on yield in a chemical process, five batches were produced...
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
34
28
27
24
29
32
36
32
32
39
21
34
32
25
35
Construct an analysis of
variance table (to 2 decimals, if necessary). Round
p-value to four decimal places.
To study the effect of temperature on yield in a chemical process, five batches were produced...
To study the effect of temperature on yield in a
chemical process, five batches were produced at each of the three
temperature level. The results follow.
50 degree C
60 degree C
70 degree C
32
31
25
22
32
30
34
35
30
37
24
32
30
28
33
A. Construct an analysis of variance table
Source Variation
Sum Squares
Degree Freedom
Mean Square
F
P-Value
Treatments
Error
Total
B. use .05 level of significance to test whether the...
To study the effect of temperature on yield in a chemical process, five batches were produced...
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
29
25
21
30
30
33
33
30
36
22
32
29
26
33
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
Error
Total
b. Use a level...
To study the effect of temperature on yield in a chemical process, five batches were produced...
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
35
28
21
36
33
33
39
33
36
28
35
29
32
36
Construct an analysis of
variance table (to 2 decimals, if necessary). Round
p-value to four decimal places.
Source of
Variation
Sum of
Squares
Degrees of
Freedom
Mean Square
F
p-value
Treatments
Error
Total
Use a .05...
To study the effect of temperature on yield in a chemical process, five batches were produced...
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
33
29
27
23
30
32
35
33
32
38
22
34
31
26
35
Construct an analysis of
variance table (to 2 decimals, if necessary). Round
p-value to four decimal places.
Source of
Variation
Sum of
Squares
Degrees of
Freedom
Mean Square
F
p-value
Treatments
Error
Total
Use a .05...
To study the effect of temperature on yield in a chemical process, five batches were produced...
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
32
20
21
33
25
33
36
25
36
25
27
29
29
28
Construct an analysis of
variance table (to 2 decimals, if necessary). Round
p-value to four decimal places.
Source of
Variation
Sum of
Squares
Degrees of
Freedom
Mean Square
F
p-value
Treatments
Error
Total
Use a .05...
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