An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in x = 18.14 kgf/cm? for the modified mortar (m = 42) and y = 16.89 kgf/cm? for the unmodified mortar (n = 30). Let u, and u, be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal. (a) Assuming that o, = 1.6 and o, = 1.3, test H: 4, - H, = 0 versus H: 4, - H, > 0 at level 0.01. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) P-value = State the conclusion in the problem context. Fail to reject Ho: The data does not suggest that the difference in average tension bond strengths exceeds from 0. Fail to reject Ho: The data suggests that the difference in average tension bond strengths exceeds 0. Reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds 0. Reject Ho: The data suggests that the difference in average tension bond strengths exceeds 0. (b) Compute the probability of a type II error for the test of part (a) when u, - H, = 1. (Round your answer to four decimal places.) (c) Suppose the investigator decided to use a level 0.05 test and wished B = 0.10 when u, - H, - 1. If m = 42, what value of n is necessary? (Round your answer up to the nearest whole number.) (d) How would the analysis and conclusion of part (a) change if o, and o, were unknown but s, = 1.6 and s, = 1.3? Since n = 30 is a large sample, it would no longer be appropriate to use the large sample test. Any other test can be used, and the conclusions would stay the same. o Since n= 30 is not a large sample, it still be appropriate use the large sample test. The analysis and conclusions would stay the same. Since n = 30 is a large sample, it would be more appropriate to use the t procedure. The appropriate conclusion would follow. Since n = 30 is not a large sample, it would no longer be appropriate to use the large sample test. A small sample t procedure should be used, and the appropriate conclusion would follow. You may need to use the appropriate table in the Appendix of Tables to answer this question.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in x = 18.14
kgf/cm2 for the modified mortar (m
42) and y = 16.89 kgf/cm2 for the unmodified mortar (n
30). Let
and
be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the
%D
bond strength distributions are both normal.
(a) Assuming that
= 1.6 and o,
1.3, test Ho: Hy-H2
O versus H: µ, - µ, > 0 at level 0.01.
Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)
Z =
P-value =
State the conclusion in the problem context.
Fail to reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds from 0.
o Fail to reject Ho. The data suggests that the difference in average tension bond strengths exceeds 0.
o Reject Ho.
The data does not suggest that the difference in average tension bond strengths exceeds 0.
o Reject Ho. The data suggests that the difference in average tension bond strengths exceeds 0.
(b) Compute the probability of a type II error for the test of part (a) when u, - µ,
= 1. (Round your answer to four decimal places.)
(c) Suppose the investigator decided to use a level 0.05 test and wished B = 0.10 when u, - u, = 1. If m = 42, what value of n is necessary? (Round your answer up to the nearest whole number.)
n =
(d) How would the analysis and conclusion of part (a) change if o, and o, were unknown but
S1
= 1.6 and
S2
= 1.3?
1
Since n = 30 is a large sample, it would no longer be appropriate to use the large sample test. Any other test can be used, and the conclusions would stay the same.
Since n = 30 is not a large sample, it still be appropriate to use the large sample test. The analysis and conclusions would stay the same.
Since n = 30 is a larg
sample, it would be
pre appropriate to use the t procedure. The
ppropriate conclusion would follow.
Since n = 30 is not a large sample, it would no longer be appropriate to use the large sample test. A small sample t procedure should be used, and the appropriate conclusion would follow.
You may need to use the appropriate table in the Appendix of Tables to answer this question.
Transcribed Image Text:An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in x = 18.14 kgf/cm2 for the modified mortar (m 42) and y = 16.89 kgf/cm2 for the unmodified mortar (n 30). Let and be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the %D bond strength distributions are both normal. (a) Assuming that = 1.6 and o, 1.3, test Ho: Hy-H2 O versus H: µ, - µ, > 0 at level 0.01. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) Z = P-value = State the conclusion in the problem context. Fail to reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds from 0. o Fail to reject Ho. The data suggests that the difference in average tension bond strengths exceeds 0. o Reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds 0. o Reject Ho. The data suggests that the difference in average tension bond strengths exceeds 0. (b) Compute the probability of a type II error for the test of part (a) when u, - µ, = 1. (Round your answer to four decimal places.) (c) Suppose the investigator decided to use a level 0.05 test and wished B = 0.10 when u, - u, = 1. If m = 42, what value of n is necessary? (Round your answer up to the nearest whole number.) n = (d) How would the analysis and conclusion of part (a) change if o, and o, were unknown but S1 = 1.6 and S2 = 1.3? 1 Since n = 30 is a large sample, it would no longer be appropriate to use the large sample test. Any other test can be used, and the conclusions would stay the same. Since n = 30 is not a large sample, it still be appropriate to use the large sample test. The analysis and conclusions would stay the same. Since n = 30 is a larg sample, it would be pre appropriate to use the t procedure. The ppropriate conclusion would follow. Since n = 30 is not a large sample, it would no longer be appropriate to use the large sample test. A small sample t procedure should be used, and the appropriate conclusion would follow. You may need to use the appropriate table in the Appendix of Tables to answer this question.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Knowledge Booster
Anova and Design of Experiments
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
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman