Homework Help is Here – Start Your Trial Now!
Math
Statistics
To test Ho: u= 40 versus H,: u< 40, a random sample of size n= 25 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= 37.4 and s = 13.6, compute the test statistic. to = - 0.956 (Round three decimal places as needed.) (b) If the researcher decides to test this hypothesis at the a = 0.05 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.)

To test Ho: u= 40 versus H,: u< 40, a random sample of size n= 25 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= 37.4 and s = 13.6, compute the test statistic. to = - 0.956 (Round three decimal places as needed.) (b) If the researcher decides to test this hypothesis at the a = 0.05 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.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question

Question 4

To test \( H_0: \mu = 40 \) versus \( H_1: \mu < 40 \), a random sample of size \( n = 25 \) is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below. [Table Icon] Click here to view the t-Distribution Area in Right Tail. **(a)** If \( \bar{x} = 37.4 \) and \( s = 13.6 \), compute the test statistic. \( t_0 = -0.956 \) (Round to three decimal places as needed.) **(b)** If the researcher decides to test this hypothesis at the \( \alpha = 0.05 \) 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.)
Transcribed Image Text:To test \( H_0: \mu = 40 \) versus \( H_1: \mu < 40 \), a random sample of size \( n = 25 \) is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below. [Table Icon] Click here to view the t-Distribution Area in Right Tail. **(a)** If \( \bar{x} = 37.4 \) and \( s = 13.6 \), compute the test statistic. \( t_0 = -0.956 \) (Round to three decimal places as needed.) **(b)** If the researcher decides to test this hypothesis at the \( \alpha = 0.05 \) 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.)
The table provided is a t-distribution table, which is used to determine the critical values of the t-distribution for hypothesis testing. This specific table shows the areas in the right tail for various degrees of freedom (df) and significance levels. ### Structure of the Table: - **Columns:** - The columns represent significance levels (α) which are the probabilities in the right tail of the t-distribution. These levels include: 0.25, 0.20, 0.15, 0.10, 0.05, 0.025, 0.02, 0.01, 0.005, 0.0025, 0.001, 0.0005. - **Rows:** - The rows represent the degrees of freedom (df). These range from 1 to 100, and then increase in increments: 120, 150, 200, 300, 500, and 1000. ### How to Use the Table: 1. **Determine the Degrees of Freedom (df):** - In hypothesis testing, the degrees of freedom are typically calculated based on your sample size. For a single sample t-test, df = n - 1, where n is the sample size. 2. **Select the Significance Level (α):** - Choose the column that corresponds to your desired significance level. This level represents the probability of rejecting the null hypothesis when it is actually true (Type I error). 3. **Find the Critical Value:** - Locate your degrees of freedom in the far left or right column. Follow across that row to the significance level column to find your critical t-value. This critical value is used to compare against your calculated t-statistic. If your t-statistic is larger than the critical value, you reject the null hypothesis. ### Example: - Suppose you are conducting a test with a significance level of 0.05 and have 15 degrees of freedom. Find the row for `df = 15` and the column for `α = 0.05`. The intersection is approximately `2.131`. This is your critical t-value. This table is essential for achieving accurate results in t-distribution related statistical analysis, and it helps quantify the certainty of your conclusions.
Transcribed Image Text:The table provided is a t-distribution table, which is used to determine the critical values of the t-distribution for hypothesis testing. This specific table shows the areas in the right tail for various degrees of freedom (df) and significance levels. ### Structure of the Table: - **Columns:** - The columns represent significance levels (α) which are the probabilities in the right tail of the t-distribution. These levels include: 0.25, 0.20, 0.15, 0.10, 0.05, 0.025, 0.02, 0.01, 0.005, 0.0025, 0.001, 0.0005. - **Rows:** - The rows represent the degrees of freedom (df). These range from 1 to 100, and then increase in increments: 120, 150, 200, 300, 500, and 1000. ### How to Use the Table: 1. **Determine the Degrees of Freedom (df):** - In hypothesis testing, the degrees of freedom are typically calculated based on your sample size. For a single sample t-test, df = n - 1, where n is the sample size. 2. **Select the Significance Level (α):** - Choose the column that corresponds to your desired significance level. This level represents the probability of rejecting the null hypothesis when it is actually true (Type I error). 3. **Find the Critical Value:** - Locate your degrees of freedom in the far left or right column. Follow across that row to the significance level column to find your critical t-value. This critical value is used to compare against your calculated t-statistic. If your t-statistic is larger than the critical value, you reject the null hypothesis. ### Example: - Suppose you are conducting a test with a significance level of 0.05 and have 15 degrees of freedom. Find the row for `df = 15` and the column for `α = 0.05`. The intersection is approximately `2.131`. This is your critical t-value. This table is essential for achieving accurate results in t-distribution related statistical analysis, and it helps quantify the certainty of your conclusions.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS