Bundle: Introduction to Statistics and Data Analysis, 5th + WebAssign Printed Access Card: Peck/Olsen/Devore. 5th Edition, Single-Term
Bundle: Introduction to Statistics and Data Analysis, 5th + WebAssign Printed Access Card: Peck/Olsen/Devore. 5th Edition, Single-Term
5th Edition
ISBN: 9781305620711
Author: Roxy Peck, Chris Olsen, Jay L. Devore
Publisher: Cengage Learning
bartleby

Videos

Question
Book Icon
Chapter 16.2, Problem 14E

a.

To determine

Test whether there is a significant difference in mean time from entry to first stroke for the two entry.

a.

Expert Solution
Check Mark

Answer to Problem 14E

The conclusion is that there is no significant difference in mean time from entry to first stroke for the two entry.

Explanation of Solution

The data based on the water entry time to the first stroke for Flat and hole.

1.

Consider μd is the mean difference in the time from the water entry to first stroke.

2.

The null hypothesis is given below:

Null hypothesis:

H0:μd=0

That is, the mean time from entry to first stroke is same for the two entry methods.

3.

The alternative hypothesis is given below:

Alternative hypothesis:

Ha:μd0

That is, the mean time from entry to first stroke is not same for the two entry methods.

4.

Test statistic:

Here, the test statistic is signed-rank sum.

5.

Critical value:

Here, the test is one-tailed test with n=10.

From Chapter 16 Appendix Table 2, the critical-value for n=10 with α=0.01 is 45.

Rejection rule:

If Signed-rank sum45(=Critical value) or Signed-rank sum45(=Critical value), then the null hypothesis is rejected.

6.

Calculation:

The difference is obtained below:

SwimmerHoleFlatDifference
11.181.060.12
21.11.23–0.13
31.311.20.11
41.121.19–0.07
51.121.29–0.17
61.231.090.14
71.271.090.18
81.081.33–0.25
91.261.27–0.01
101.271.38–0.11

Ordering the absolute differences results in the following assignment of signed ranks.

DifferenceSigned Rank
0.01–1
0.07–2
0.11–3.5
0.113.5
0.125
0.13–6
0.147
0.17–8
0.189
0.25–10

The test statistic is,

Signed-rank sum=123.5+3.5+56+78+910=6

Thus, the test statistic is –6.

7.

Conclusion:

Here, the signed-rank sum is greater than the critical value.

That is, 6(=Signed-rank sum)45(=Critical value).

By the rejection rule, the null hypothesis is not rejected.

Thus, there is no significant difference in mean time from entry to first stroke for the two entry.

b.

To determine

Test whether the data suggest a difference in mean initial velocity for the two entry methods.

b.

Expert Solution
Check Mark

Answer to Problem 14E

The conclusion is that there is no evidence that the data suggest a difference in mean initial velocity for the two entry methods.

Explanation of Solution

The data based on the initial velocity for the Flat and hole.

1.

Consider μd is the difference in mean time from entry to first stroke for the two entry.

2.

The null hypothesis is given below:

Null hypothesis:

H0:μd=0

That is, the mean initial velocity is same for the two entry methods.

3.

The alternative hypothesis is given below:

Alternative hypothesis:

Ha:μd0

That is, the mean initial velocity is not same for the two entry methods.

4.

Test statistic:

Here, the test statistic is signed-rank sum.

5.

Critical value:

Here, the test is one-tailed test with n=10.

From Chapter 16 Appendix Table 2, the critical-value for n=10 with α=0.01 is 45.

Rejection rule:

If Signed-rank sum45(=Critical value) or Signed-rank sum45(=Critical value), then the null hypothesis is rejected.

6.

Calculation:

The difference is obtained below:

SwimmerHoleFlatDifference
12425.1–1.1
222.522.40.1
321.624–2.4
421.422.4–1
520.923.9–3
620.821.7–0.9
722.423.8–1.4
822.922.90
923.325–1.7
1020.719.51.2

Ordering the absolute differences results in the following assignment of signed ranks.

DifferenceSigned Rank
0-
0.11
0.9–2
1–3
1.1–4
1.25
1.4–6
1.7–7
2.4–8
3–9

The test statistic is,

Signed-rank sum=1234+56789=33

Thus, the test statistic is –33.

7.

Conclusion:

Here, the signed-rank sum is greater than the critical value.

That is, 33(=Signed-rank sum)45(=Critical value).

By the rejection rule, the null hypothesis is not rejected.

Thus, there is no evidence that the data suggest a difference in mean initial velocity for the two entry methods.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Given the following sample data values: 7, 12, 15, 9, 15, 13, 12, 10, 18,12 Find the following: a) Σ x= b) x² = c) x = n d) Median = e) Midrange x = (Enter a whole number) (Enter a whole number) (use one decimal place accuracy) (use one decimal place accuracy) (use one decimal place accuracy) f) the range= g) the variance, s² (Enter a whole number) f) Standard Deviation, s = (use one decimal place accuracy) Use the formula s² ·Σx² -(x)² n(n-1) nΣ x²-(x)² 2 Use the formula s = n(n-1) (use one decimal place accuracy)
Table of hours of television watched per week: 11 15 24 34 36 22 20 30 12 32 24 36 42 36 42 26 37 39 48 35 26 29 27 81276 40 54 47 KARKE 31 35 42 75 35 46 36 42 65 28 54 65 28 23 28 23669 34 43 35 36 16 19 19 28212 Using the data above, construct a frequency table according the following classes: Number of Hours Frequency Relative Frequency 10-19 20-29 |30-39 40-49 50-59 60-69 70-79 80-89 From the frequency table above, find a) the lower class limits b) the upper class limits c) the class width d) the class boundaries Statistics 300 Frequency Tables and Pictures of Data, page 2 Using your frequency table, construct a frequency and a relative frequency histogram labeling both axes.
Table of hours of television watched per week: 11 15 24 34 36 22 20 30 12 32 24 36 42 36 42 26 37 39 48 35 26 29 27 81276 40 54 47 KARKE 31 35 42 75 35 46 36 42 65 28 54 65 28 23 28 23669 34 43 35 36 16 19 19 28212 Using the data above, construct a frequency table according the following classes: Number of Hours Frequency Relative Frequency 10-19 20-29 |30-39 40-49 50-59 60-69 70-79 80-89 From the frequency table above, find a) the lower class limits b) the upper class limits c) the class width d) the class boundaries Statistics 300 Frequency Tables and Pictures of Data, page 2 Using your frequency table, construct a frequency and a relative frequency histogram labeling both axes.
Knowledge Booster
Background pattern image
Statistics
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
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Text book image
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Text book image
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
What Are Research Ethics?; Author: HighSchoolScience101;https://www.youtube.com/watch?v=nX4c3V23DZI;License: Standard YouTube License, CC-BY
What is Ethics in Research - ethics in research (research ethics); Author: Chee-Onn Leong;https://www.youtube.com/watch?v=W8Vk0sXtMGU;License: Standard YouTube License, CC-BY