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To test Ho: H= 20 versus H,: u< 20, a simple random sample of size n= 16 is obtained from a population that is known to be normally distributed. Answer parts (a)-(d). O Click here to view the t-Distribution Area in Right Tail. (a) If x = 18 and s = 4.3, compute the test statistic. t= - 1.86 (Round to two decimal places as needed.) (b) Draw a t-distribution with the area that represents the P-value shaded. Which of the following graphs shows the correct shaded region? OA. в. C.

To test Ho: H= 20 versus H,: u< 20, a simple random sample of size n= 16 is obtained from a population that is known to be normally distributed. Answer parts (a)-(d). O Click here to view the t-Distribution Area in Right Tail. (a) If x = 18 and s = 4.3, compute the test statistic. t= - 1.86 (Round to two decimal places as needed.) (b) Draw a t-distribution with the area that represents the P-value shaded. Which of the following graphs shows the correct shaded region? OA. в. C.

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
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**t-Distribution Table: Area in Right Tail** This table provides critical values of the t-distribution, commonly used in statistical analyses, especially for hypothesis testing and confidence intervals. The table is organized to show the area in the right tail for various degrees of freedom (df) and probability levels. **Columns: Probability Levels** Each column represents a certain level of probability for the right tail (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: Degrees of Freedom (df)** The rows correspond to degrees of freedom ranging from 1 to 100, including commonly used specific values like 30, 40, 60, 90, and 1000. **Values** - The intersection between a row (df) and a column (probability level) shows the critical t-value for that specific configuration. - For example, at 5 degrees of freedom and a 0.05 probability level, the t-value is 2.015. This t-distribution table helps determine the threshold t-value needed to evaluate statistical significance for different sample sizes (degrees of freedom) and confidence levels (probability).
Transcribed Image Text:**t-Distribution Table: Area in Right Tail** This table provides critical values of the t-distribution, commonly used in statistical analyses, especially for hypothesis testing and confidence intervals. The table is organized to show the area in the right tail for various degrees of freedom (df) and probability levels. **Columns: Probability Levels** Each column represents a certain level of probability for the right tail (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: Degrees of Freedom (df)** The rows correspond to degrees of freedom ranging from 1 to 100, including commonly used specific values like 30, 40, 60, 90, and 1000. **Values** - The intersection between a row (df) and a column (probability level) shows the critical t-value for that specific configuration. - For example, at 5 degrees of freedom and a 0.05 probability level, the t-value is 2.015. This t-distribution table helps determine the threshold t-value needed to evaluate statistical significance for different sample sizes (degrees of freedom) and confidence levels (probability).
To test \( H_0: \mu = 20 \) versus \( H_1: \mu < 20 \), a simple random sample of size \( n = 16 \) is obtained from a population that is known to be normally distributed. Answer parts (a)-(d). Click here to view the t-Distribution Area in Right Tail. (a) If \( \bar{x} = 18 \) and \( s = 4.3 \), compute the test statistic. \( t = -1.86 \) (Round to two decimal places as needed.) (b) Draw a t-distribution with the area that represents the P-value shaded. Which of the following graphs shows the correct shaded region? - **Option A:** A graph showing a t-distribution curve with shading in the left tail. - **Option B:** A graph showing a t-distribution curve with no visible shading. - **Option C:** A graph showing a t-distribution curve with shading in both tails.
Transcribed Image Text:To test \( H_0: \mu = 20 \) versus \( H_1: \mu < 20 \), a simple random sample of size \( n = 16 \) is obtained from a population that is known to be normally distributed. Answer parts (a)-(d). Click here to view the t-Distribution Area in Right Tail. (a) If \( \bar{x} = 18 \) and \( s = 4.3 \), compute the test statistic. \( t = -1.86 \) (Round to two decimal places as needed.) (b) Draw a t-distribution with the area that represents the P-value shaded. Which of the following graphs shows the correct shaded region? - **Option A:** A graph showing a t-distribution curve with shading in the left tail. - **Option B:** A graph showing a t-distribution curve with no visible shading. - **Option C:** A graph showing a t-distribution curve with shading in both tails.
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