Question

Anela is a computer scientist who is formulating a large and complicated program for a type of data processing. She has three ways of storing and retrieving data: cloud storage, disk, or hard drive. As an experiment, she sets up her program in three different ways: one using cloud storage, one using disks, and the other using a hard drive. Then she makes four test runs of this type of data processing on each program. The time required to execute each program is shown in the following table (in minutes). Use a 0.01 level of significance to test the hypothesis that the mean processing time is the same for each method.

Hard Drive	Cloud	Disks
8.4	7.6	6.8
9.5	9.2	6.5
8.4	7.4	10.2
8.3	7.4	8.3

Classify the problem as being a Chi-square test of independence or homogeneity, Chi-square goodness-of-fit, Chi-square for testing or estimating σ² or σ, F test for two variances, One-way ANOVA, or Two-way ANOVA, then perform the following.

Chi-square test of independence or homogeneityF test for two variances    Chi-square for testing or estimating σ² or σTwo-way ANOVAChi-square goodness-of-fitOne-way ANOVA

(i) Give the value of the level of significance.


State the null and alternate hypotheses.

H₀: μ₁ = μ₂ = μ₃; H₁: All three means are equal.H₀: μ₁ = μ₂ = μ₃; H₁: All three means are different.    H₀: μ₁ = μ₂ = μ₃; H₁: Not all the means are equal.H₀: μ₁ = μ₂ = μ₃; H₁: Exactly two means are equal.

(ii) Find the sample test statistic. (Round your F Ratio to two decimal places. Round all other answers to four decimal places.)


(iii) Find the P-value of the sample test statistic.

P-value > 0.1000.050 < P-value < 0.100    0.025 < P-value < 0.0500.010 < P-value < 0.0250.001 < P-value < 0.010P-value < 0.001

(iv) Conclude the test.

Since the P-value is greater than or equal to the level of significance at α = 0.01, we do not reject H₀.Since the P-value is less than the level of significance at α = 0.01, we reject H₀.    Since the P-value is greater than or equal to the level of significance at α = 0.01, we reject H₀.Since the P-value is less than the level of significance at α = 0.01, we do not reject H₀.

(v) Interpret the conclusion in the context of the application.

At the 1% level of significance there is insufficient evidence to conclude that the mean times to execute the programs are not all equal.At the 1% level of significance there is sufficient evidence to conclude that the mean times to execute the programs are equal.    At the 1% level of significance there is insufficient evidence to conclude that the mean times to execute the programs are equal.At the 1% level of significance there is sufficient evidence to conclude that the mean times to execute the programs are not all equal.

(vi) In the case of one-way ANOVA, make a summary table. (Round your answers to three decimal places.)

Source of Variation	Sum of Squares	Degrees of Freedom	MS	F Ratio	P-Value	Test Decision
Between groups					---Select--- P-value > 0.100 0.050 < P-value < 0.100 0.025 < P-value < 0.050 0.010 < P-value < 0.025 0.001 < P-value < 0.010 P-value < 0.001	---Select--- Do not reject H0. Reject H0.
Within groups
Total

Answer 1

answered by: anonymous