Medical research has shown that repeated wrist extension beyond 20 degrees increases the risk of wrist and hand injuries. Each of 24 students at a university used a proposed new computer mouse design, and while using the mouse, each student's wrist extension was recorded. Data consistent with summary values given in a paper are shown. Use these data with the resulting sample mean 25.750000 and sample standard deviation 1.870829, to test the hypothesis that the mean wrist extension for people using this new mouse design is greater than 20 degrees. (Use = 0.05.) 27 22 OH μ-20 HJ μ<20 t = 25 26 28 24 26 25 State the appropriate null and altemative hypotheses. OH μ<20 Haka 20 OH μ-20 HH* 20 P-value= 27 27 24 28 О Нj u - 20 Hà 120 OH μ>20 H <20 Find the test statistic and P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.) 24 26 26 26 24 25 31 24 25 27 27 24 State your conclusion. O We reject Ho. We do not have convincing evidence that the mean wrist extension for all people using the new mouse design is greater than 20 degrees. O We reject Ho. We have convincing evidence that the mean wrist extension for all people using the new mouse design is greater than 20 degrees. O We fail to reject Ho. We have convincing evidence that the mean wrist extension for all people using the new mouse design is greater than 20 degrees. O We fail to reject Ho. We do not have convincing evidence that the mean wrist extension for all people using the new mouse design is greater than 20 degrees. Are any assumptions required in order for it to be appropriate to generalize the results of your test to the population of students from this university? O We need to assume that the 24 students used in the study are representative of all students with a history of wrist or hand injuries. O We need to assume that the 24 students used in the study are representative of all students in computer science classes. O We need to assume that the 24 students used in the study are representative of all students who own PCs O We need to assume that the 24 students used in the study are representative of all students at the university We need to assume that the 24 students used in the study are representative of all students who use a wireless mouse.
Medical research has shown that repeated wrist extension beyond 20 degrees increases the risk of wrist and hand injuries. Each of 24 students at a university used a proposed new computer mouse design, and while using the mouse, each student's wrist extension was recorded. Data consistent with summary values given in a paper are shown. Use these data with the resulting sample mean 25.750000 and sample standard deviation 1.870829, to test the hypothesis that the mean wrist extension for people using this new mouse design is greater than 20 degrees. (Use = 0.05.) 27 22 OH μ-20 HJ μ<20 t = 25 26 28 24 26 25 State the appropriate null and altemative hypotheses. OH μ<20 Haka 20 OH μ-20 HH* 20 P-value= 27 27 24 28 О Нj u - 20 Hà 120 OH μ>20 H <20 Find the test statistic and P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.) 24 26 26 26 24 25 31 24 25 27 27 24 State your conclusion. O We reject Ho. We do not have convincing evidence that the mean wrist extension for all people using the new mouse design is greater than 20 degrees. O We reject Ho. We have convincing evidence that the mean wrist extension for all people using the new mouse design is greater than 20 degrees. O We fail to reject Ho. We have convincing evidence that the mean wrist extension for all people using the new mouse design is greater than 20 degrees. O We fail to reject Ho. We do not have convincing evidence that the mean wrist extension for all people using the new mouse design is greater than 20 degrees. Are any assumptions required in order for it to be appropriate to generalize the results of your test to the population of students from this university? O We need to assume that the 24 students used in the study are representative of all students with a history of wrist or hand injuries. O We need to assume that the 24 students used in the study are representative of all students in computer science classes. O We need to assume that the 24 students used in the study are representative of all students who own PCs O We need to assume that the 24 students used in the study are representative of all students at the university We need to assume that the 24 students used in the study are representative of all students who use a wireless mouse.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:**Research Study on Wrist Extension and Computer Mouse Design**
Medical research has indicated that repeated wrist extension beyond 20 degrees increases the risk of wrist and hand injuries. A study was conducted with 24 university students using a proposed new computer mouse design. While using the mouse, each student's wrist extension was recorded. Below are the summary data:
Recorded Wrist Extensions (Degrees):
27, 25, 26, 28, 27, 24, 24, 26, 26, 24, 23, 25
22, 24, 26, 25, 28, 27, 24, 31, 24, 25, 27, 24
*Sample Mean*: 25.750000
*Sample Standard Deviation*: 1.870829
**Hypothesis Testing**
The aim is to test the hypothesis that the mean wrist extension for people using this new mouse design is greater than 20 degrees (α = 0.05).
**Select the Appropriate Null and Alternative Hypotheses:**
- \( H_0: \mu < 20 \) vs \( H_a: \mu \geq 20 \)
- \( H_0: \mu = 20 \) vs \( H_a: \mu > 20 \)
- \( H_0: \mu = 20 \) vs \( H_a: \mu < 20 \)
- \( H_0: \mu \geq 20 \) vs \( H_a: \mu < 20 \)
- \( H_0: \mu > 20 \) vs \( H_a: \mu \leq 20 \)
- \( H_0: \mu \leq 20 \) vs \( H_a: \mu > 20 \)
- \( H_0: \mu > 20 \) vs \( H_a: \mu = 20 \)
**Calculate the Test Statistic and P-value:**
- *t* = _______
- *P-value* = _______
**State Your Conclusion:**
- Reject \( H_0 \). We do not have convincing evidence that the mean wrist extension for all people using the new mouse design is greater than 20 degrees.
- Reject \( H_0 \). We have convincing evidence that the mean wrist extension for all people using the new mouse design is greater than 20 degrees.
- Fail to reject \(
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