Question

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	30	22
24	30	28
35	35	27
38	24	30
30	21	28

Construct an analysis of variance table. (Round your values for MSE and F to two decimal places, and your 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 0.05 level of significance to test whether the temperature level has an effect on the mean yield of the process.

State the null and alternative hypotheses.

H₀: Not all the population means are equal.
H_a: μ_50°C = μ_60°C = μ_70°CH₀: μ_50°C = μ_60°C = μ_70°C
H_a: Not all the population means are equal.    H₀: At least two of the population means are equal.
H_a: At least two of the population means are different.H₀: μ_50°C = μ_60°C = μ_70°C
H_a: μ_50°C ≠ μ_60°C ≠ μ_70°CH₀: μ_50°C ≠ μ_60°C ≠ μ_70°C
H_a: μ_50°C = μ_60°C = μ_70°C

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

Reject H₀. There is not sufficient evidence to conclude that the mean yields for the three temperatures are not equal.Reject H₀. There is sufficient evidence to conclude that the mean yields for the three temperatures are not equal.    Do not reject H₀. There is sufficient evidence to conclude that the mean yields for the three temperatures are not equal.Do not reject H₀. There is not sufficient evidence to conclude that the mean yields for the three temperatures are not equal.

Answer 1

The statistical software output for this problem is:

Hence,

ANOVA table:

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
Treatments	70	2	35	1.54	0.2531
Error	272	12	22.67
Total	342	14

Hypotheses:

H₀: μ_50°C = μ_60°C = μ_70°C

H_a: Not all the population means are equal.

Test statistic = 1.54

P - value = 0.2531

Do not reject H₀. There is not sufficient evidence to conclude that the mean yields for the three temperatures are not equal. Option D is correct.