To test Ho: u= 100 versus H,: u# 100, a simple random sample size of n=22 is obtained from a population that is known to be normally distributed. Answer parts (a)-(d). E Click here to view the t-Distribution Area in Right Tail. T-distribution area in right tail (a) If x = 105.4 and s = 9.6, compute the test statistic. t= (Round to three decimal places as needed.) t-Distribution ni-kt Til
To test Ho: u= 100 versus H,: u# 100, a simple random sample size of n=22 is obtained from a population that is known to be normally distributed. Answer parts (a)-(d). E Click here to view the t-Distribution Area in Right Tail. T-distribution area in right tail (a) If x = 105.4 and s = 9.6, compute the test statistic. t= (Round to three decimal places as needed.) t-Distribution ni-kt Til
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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![To test \( H_0: \mu = 100 \) versus \( H_1: \mu \neq 100 \), a simple random sample size of \( n = 22 \) is obtained from a population that is known to be normally distributed. Answer parts (a)-(d).
**(a)** If \( \bar{x} = 105.4 \) and \( s = 9.6 \), compute the test statistic.
\[ t = \, \_\_\_ \quad (\text{Round to three decimal places as needed.}) \]
---
**T-distribution Area in Right Tail**
The accompanying diagram displays a table of the t-distribution area in the right tail. This table is crucial for determining the critical values of t for various significance levels and degrees of freedom (df).
- **Degrees of Freedom (df):** The leftmost and rightmost columns provide the degrees of freedom, ranging from 1 to 31.
- **Columns of Significance Levels:** The columns from left to right denote different significance levels of the t-distribution tail area (e.g., 0.25, 0.20, 0.15, etc.), with some extremely small values such as 0.001 and 0.0005.
- **Entries:** The table shows critical t-values corresponding to each combination of degrees of freedom and tail area.
In this table, the critical t-values decrease as the degrees of freedom increase, indicating a shift towards a normal distribution as the sample size grows. This tool is used for hypothesis testing by comparing the computed t-statistic against these critical values to determine if the null hypothesis can be rejected.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca33379b-88dc-4620-8e0a-110bf0c38b46%2Ff0bfcb41-1ed4-4367-b7b9-2542920b963f%2Ftq0in9_processed.png&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 \( n = 22 \) is obtained from a population that is known to be normally distributed. Answer parts (a)-(d).
**(a)** If \( \bar{x} = 105.4 \) and \( s = 9.6 \), compute the test statistic.
\[ t = \, \_\_\_ \quad (\text{Round to three decimal places as needed.}) \]
---
**T-distribution Area in Right Tail**
The accompanying diagram displays a table of the t-distribution area in the right tail. This table is crucial for determining the critical values of t for various significance levels and degrees of freedom (df).
- **Degrees of Freedom (df):** The leftmost and rightmost columns provide the degrees of freedom, ranging from 1 to 31.
- **Columns of Significance Levels:** The columns from left to right denote different significance levels of the t-distribution tail area (e.g., 0.25, 0.20, 0.15, etc.), with some extremely small values such as 0.001 and 0.0005.
- **Entries:** The table shows critical t-values corresponding to each combination of degrees of freedom and tail area.
In this table, the critical t-values decrease as the degrees of freedom increase, indicating a shift towards a normal distribution as the sample size grows. This tool is used for hypothesis testing by comparing the computed t-statistic against these critical values to determine if the null hypothesis can be rejected.
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