(a) If x= 104.4 and s 8.6, compute the test statistic, (Round to three decimal places as needed.) (b) If the researcher decides to test this hypothesis at the a= 0.01 level of significance, determine the critical values. The critical values are. (Use a comma to separate answers as needed. Round to three decimal places as needed.) (c) Draw a t-distribution that depicts the critical region(s). Which of the following graphs shows the critical region(s) in the t-distribution? O A. OB. (d) Will the researcher reject the null hypothesis?
(a) If x= 104.4 and s 8.6, compute the test statistic, (Round to three decimal places as needed.) (b) If the researcher decides to test this hypothesis at the a= 0.01 level of significance, determine the critical values. The critical values are. (Use a comma to separate answers as needed. Round to three decimal places as needed.) (c) Draw a t-distribution that depicts the critical region(s). Which of the following graphs shows the critical region(s) in the t-distribution? O A. OB. (d) Will the researcher reject the null hypothesis?
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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Question
![To test \( H_0: \mu = 100 \) versus \( H_1: \mu \neq 100 \), a simple random sample was taken.
Click here to view the t-Distribution Area in Right Tail.
---
(a) If \(\bar{x} = 104.4\) and \(s = 8.6\), compute the test statistic.
\[ t = \] (Round to three decimal places as needed.)
(b) If the researcher decides to test this hypothesis at the \( \alpha = 0.10 \) level of significance, the critical values are
\[ \] (Use a comma to separate answers as needed. Round to three decimal places as needed.)
(c) Draw a t-distribution that depicts the critical region(s). Which graph shows the correct region?
- \( \circ \) A.
A bell curve is shown to represent the distribution.
---
(d) Will the researcher reject the null hypothesis?
- \( \circ \) A. There is not sufficient evidence for the researcher to reject the null hypothesis.
- \( \circ \) B. The researcher will reject the null hypothesis since the test statistic is not in the critical region.
- \( \circ \) C. There is not sufficient evidence for the researcher to accept the null hypothesis.
- \( \circ \) D. The researcher will reject the null hypothesis since the test statistic is in the critical region.
---
**Table: T-distribution area in right tail**
The table shows the critical values of the t-distribution for various degrees of freedom (df) and right-tail area probabilities. The columns represent different probabilities (0.25, 0.20, 0.15, 0.10, 0.05, 0.025, 0.02, 0.01, 0.005, 0.0025, 0.001, 0.0005), while the rows represent degrees of freedom ranging from 1 to 30. Values increase as the probability decreases, matching the expected behavior of t-distribution critical values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77aea7c1-e1b0-47d1-a611-3ed1fc1f706d%2F92b557cc-859e-40f5-81cc-365b6fbaddaf%2F88cg07g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:To test \( H_0: \mu = 100 \) versus \( H_1: \mu \neq 100 \), a simple random sample was taken.
Click here to view the t-Distribution Area in Right Tail.
---
(a) If \(\bar{x} = 104.4\) and \(s = 8.6\), compute the test statistic.
\[ t = \] (Round to three decimal places as needed.)
(b) If the researcher decides to test this hypothesis at the \( \alpha = 0.10 \) level of significance, the critical values are
\[ \] (Use a comma to separate answers as needed. Round to three decimal places as needed.)
(c) Draw a t-distribution that depicts the critical region(s). Which graph shows the correct region?
- \( \circ \) A.
A bell curve is shown to represent the distribution.
---
(d) Will the researcher reject the null hypothesis?
- \( \circ \) A. There is not sufficient evidence for the researcher to reject the null hypothesis.
- \( \circ \) B. The researcher will reject the null hypothesis since the test statistic is not in the critical region.
- \( \circ \) C. There is not sufficient evidence for the researcher to accept the null hypothesis.
- \( \circ \) D. The researcher will reject the null hypothesis since the test statistic is in the critical region.
---
**Table: T-distribution area in right tail**
The table shows the critical values of the t-distribution for various degrees of freedom (df) and right-tail area probabilities. The columns represent different probabilities (0.25, 0.20, 0.15, 0.10, 0.05, 0.025, 0.02, 0.01, 0.005, 0.0025, 0.001, 0.0005), while the rows represent degrees of freedom ranging from 1 to 30. Values increase as the probability decreases, matching the expected behavior of t-distribution critical values.
![To test \( H_0: \mu = 100 \) versus \( H_1: \mu \neq 100 \), a simple random sample size of \( n = 18 \) is obtained from a normally distributed population. Answer parts (a)-(d).
(a) If \( \bar{x} = 104.4 \) and \( s = 8.6 \), compute the test statistic.
\[ t = \frac{\bar{x} - \mu}{s / \sqrt{n}} \]
(Round to three decimal places as needed.)
(b) If the researcher decides to test this hypothesis at the \( \alpha = 0.01 \) level of significance, determine the critical values.
The critical values are \([ \, ]\).
(Use a comma to separate answers as needed. Round to three decimal places as needed.)
(c) Draw a t-distribution that depicts the critical region(s). Which of the following graphs shows the critical region(s) in the t-distribution?
- **Graph A:** Displays a t-distribution curve with shaded areas at both tails, representing critical regions.
- **Graph B:** Displays a t-distribution curve with shaded areas mainly at the right tail.
- **Graph C:** Displays a t-distribution curve with shaded areas predominantly at the left tail.
(d) Will the researcher reject the null hypothesis?
A. There is not sufficient evidence for the researcher to reject the null hypothesis since the test statistic is not between the critical values.
B. The researcher will reject the null hypothesis since the test statistic is between the critical values.
C. There is not sufficient evidence for the researcher to reject the null hypothesis since the test statistic is between the critical values.
D. The researcher will reject the null hypothesis since the test statistic is not between the critical values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77aea7c1-e1b0-47d1-a611-3ed1fc1f706d%2F92b557cc-859e-40f5-81cc-365b6fbaddaf%2Fbhtwi5vj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:To test \( H_0: \mu = 100 \) versus \( H_1: \mu \neq 100 \), a simple random sample size of \( n = 18 \) is obtained from a normally distributed population. Answer parts (a)-(d).
(a) If \( \bar{x} = 104.4 \) and \( s = 8.6 \), compute the test statistic.
\[ t = \frac{\bar{x} - \mu}{s / \sqrt{n}} \]
(Round to three decimal places as needed.)
(b) If the researcher decides to test this hypothesis at the \( \alpha = 0.01 \) level of significance, determine the critical values.
The critical values are \([ \, ]\).
(Use a comma to separate answers as needed. Round to three decimal places as needed.)
(c) Draw a t-distribution that depicts the critical region(s). Which of the following graphs shows the critical region(s) in the t-distribution?
- **Graph A:** Displays a t-distribution curve with shaded areas at both tails, representing critical regions.
- **Graph B:** Displays a t-distribution curve with shaded areas mainly at the right tail.
- **Graph C:** Displays a t-distribution curve with shaded areas predominantly at the left tail.
(d) Will the researcher reject the null hypothesis?
A. There is not sufficient evidence for the researcher to reject the null hypothesis since the test statistic is not between the critical values.
B. The researcher will reject the null hypothesis since the test statistic is between the critical values.
C. There is not sufficient evidence for the researcher to reject the null hypothesis since the test statistic is between the critical values.
D. The researcher will reject the null hypothesis since the test statistic is not between the critical values.
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