A modification has been made to the process for producing a certain type of film. Because the modification involves extra cost, it will be incorporated only if sample data provide evidence that the modification decreases mean developing time by more than 2 seconds. Assuming that the developing-time distributions have the same shape and variability, use the rank-sum test, a significance level of 0.05, and the following data to test the appropriate hypotheses. (Use μ1 for the original process and μ2 for the modified process.) Original process 8.2 5.3 4.6 5.7 6.9 6.2 5.5 8.6 Modified process 5.6 4.0 3.4 6.0 5.4 4.8 7.0 5.5 State the null and alternative hypotheses. H0: μ1 − μ2 = 0 Ha: μ1 − μ2 > 0 H0: μ1 − μ2 = 2 Ha: μ1 − μ2 < 2 H0: μ1 − μ2 = 0 Ha: μ1 − μ2 < 0 H0: μ1 − μ2 = 2 Ha: μ1 − μ2 ≠ 2 H0: μ1 − μ2 = 2 Ha: μ1 − μ2 > 2 Calculate the test statistic. rank sum = What is the P-value for this test? P-value < 0.010 .01 < P-value < 0.05 P-value > 0.05 What can you conclude? Reject H0. The data do not provide convincing evidence that the modification decreases mean developing time by more than 2 seconds. Fail to reject H0. The data provide convincing evidence that the modification decreases mean developing time by more than 2 seconds. Reject H0. The data provide convincing evidence that the modification decreases mean developing time by more than 2 seconds. Fail to reject H0. The data do not provide convincing evidence that the modification decreases mean developing time by more than 2 seconds.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

A modification has been made to the process for producing a certain type of film. Because the modification involves extra cost, it will be incorporated only if sample data provide evidence that the modification decreases mean developing time by more than 2 seconds. Assuming that the developing-time distributions have the same shape and variability, use the rank-sum test, a significance level of 0.05, and the following data to test the appropriate hypotheses. (Use μ₁ for the original process and μ₂ for the modified process.)

Original process	8.2	5.3	4.6	5.7	6.9	6.2	5.5	8.6
Modified process	5.6	4.0	3.4	6.0	5.4	4.8	7.0	5.5

State the null and alternative hypotheses.

H₀: μ₁ − μ₂ = 0

H_a: μ₁ − μ₂ > 0

H₀: μ₁ − μ₂ = 2

H_a: μ₁ − μ₂ < 2

H₀: μ₁ − μ₂ = 0

H_a: μ₁ − μ₂ < 0

H₀: μ₁ − μ₂ = 2

H_a: μ₁ − μ₂ ≠ 2

H₀: μ₁ − μ₂ = 2

H_a: μ₁ − μ₂ > 2

Calculate the test statistic.

rank sum =

What is the P-value for this test?

P-value < 0.010

.01 < P-value < 0.05

P-value > 0.05

What can you conclude?

Reject H₀. The data do not provide convincing evidence that the modification decreases mean developing time by more than 2 seconds.

Fail to reject H₀. The data provide convincing evidence that the modification decreases mean developing time by more than 2 seconds.

Reject H₀. The data provide convincing evidence that the modification decreases mean developing time by more than 2 seconds.

Fail to reject H₀. The data do not provide convincing evidence that the modification decreases mean developing time by more than 2 seconds.

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 7 steps with 8 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Non-parametric Tests$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions