To test Ho: µ= 40 versus H4: µ< 40, a random sample of size n = 26 is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below. E Click here to view the t-Distribution Area in Right Tail. a) If x= 37.2 and s= 14.9, compute the test statistic. n = - .958 (Round to three decimal places as needed.) b) If the researcher decides to test this hypothesis at the a = 0.1 level of significance, determine the critical value(s). Although technology or a t-distribution table can be used to find the critical value, n this problem use the t-distribution table given. Critical Value: Round to three decimal places. Use a comma to separate answers as needed.)
To test Ho: µ= 40 versus H4: µ< 40, a random sample of size n = 26 is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below. E Click here to view the t-Distribution Area in Right Tail. a) If x= 37.2 and s= 14.9, compute the test statistic. n = - .958 (Round to three decimal places as needed.) b) If the researcher decides to test this hypothesis at the a = 0.1 level of significance, determine the critical value(s). Although technology or a t-distribution table can be used to find the critical value, n this problem use the t-distribution table given. Critical Value: Round to three decimal places. Use a comma to separate answers as needed.)
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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Problem 1P
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Transcribed Image Text:**t-Distribution Table**
*Area in Right Tail*
This table provides critical values of the t-distribution for various significance levels in the right tail. The table is organized based on degrees of freedom (df), ranging from 1 to 1000. Critical t-values are provided for areas (probabilities) of 0.25, 0.20, 0.15, 0.10, 0.05, 0.025, 0.02, 0.01, 0.005, 0.0025, 0.001, 0.0005.
- **Degrees of Freedom (df):** Located in the first and last columns, this ranges from 1 to 40, with select values continuing to 1000.
- **Probability Levels:** Displayed at the top and bottom of the table, representing the area in the right tail of the t-distribution.
For example, with 5 degrees of freedom and an area of 0.05 in the right tail, the critical t-value is 2.571.
The values across the row represent increasing critical values as the confidence level becomes stricter (e.g., from 0.25 to 0.0005). As the degrees of freedom increase, the critical t-values generally decrease, reflecting the convergence to the normal distribution.
![**T-Test for a Sample Mean**
To test \( H_0: \mu = 40 \) versus \( H_1: \mu < 40 \), a random sample of size \( n = 26 \) is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below.
---
**(a)** If \( \bar{x} = 37.2 \) and \( s = 14.9 \), compute the test statistic.
\[ t_0 = -0.958 \] (Round to three decimal places as needed.)
---
**(b)** If the researcher decides to test this hypothesis at the \( \alpha = 0.1 \) level of significance, determine the critical value(s). Although technology or a t-distribution table can be used to find the critical value, in this problem use the t-distribution table given.
Critical Value: \[ \_\_\_\_\_\_ \]
(Round to three decimal places. Use a comma to separate answers as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1abf5c35-9136-475d-aa34-57d94fb3cf0e%2F9a3b43ff-4f42-4c0f-b4fa-9a76216eedb0%2Fz7629ud_processed.png&w=3840&q=75)
Transcribed Image Text:**T-Test for a Sample Mean**
To test \( H_0: \mu = 40 \) versus \( H_1: \mu < 40 \), a random sample of size \( n = 26 \) is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below.
---
**(a)** If \( \bar{x} = 37.2 \) and \( s = 14.9 \), compute the test statistic.
\[ t_0 = -0.958 \] (Round to three decimal places as needed.)
---
**(b)** If the researcher decides to test this hypothesis at the \( \alpha = 0.1 \) level of significance, determine the critical value(s). Although technology or a t-distribution table can be used to find the critical value, in this problem use the t-distribution table given.
Critical Value: \[ \_\_\_\_\_\_ \]
(Round to three decimal places. Use a comma to separate answers as needed.)
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