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(a) Use the summary to determine the point estimate of the population mean and margin of error for the confidence interval.

(a) Use the summary to determine the point estimate of the population mean and margin of error for the confidence interval.

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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The image contains a summary and questions from a study on the ages when respondents first married. Here's the transcription: --- **7. A study asked respondents, "If ever married, how old were you when you first married?" The results are summarized in the technology excerpt that follows. Complete parts (a) through (d) below.** **One-Sample T: AGEWED** | Variable | N | Mean | StDev | SE Mean | 95.0% CI | |----------|------|-------|-------|---------|-------------------| | AGEWED | 26910| 23.370| 4.714 | 0.029 | (23.314, 23.426) | 13 Click the icon to view the table of critical t-values. (a) Use the summary to determine the point estimate of the population mean and margin of error for the confidence interval. - \( \bar{x} = \_\_\_\_\_\_\_\_\_ \) (Type an integer or a decimal. Do not round.) - \( E = \_\_\_\_\_\_\_\_\_ \) (Type an integer or a decimal. Do not round.) (b) Interpret the confidence interval. - O A. One can be 95% confident that the mean age of people when first married is 23.370 years. - O B. One can be 95% confident that the mean age of people when first married is between 23.314 and 23.426 years. - O C. There is a 95% probability that the mean age of people when first married is between 23.314 and 23.426 years. - O D. There is a 95% probability that the mean age of people when first married is 23.370 years. (c) Verify the results by computing a 95% confidence interval with the information provided. Begin with the lower bound. \[\_\_\_\_\_\_\_\_\_\_\_\_\_\_ (1) \times \_\_\_\_\_\_\_\_\_\_\_\_ \cdot 4.714 = \_\_\_\_\_\_\_\_\_\_\_\] (Round to three decimal places as needed.) Next find the upper bound. \[\_\_\_\_\_\_\_\_\_\_\_\_\_\_ (2) \times \_\_\_\_\_\_\_\_\_\
Transcribed Image Text:The image contains a summary and questions from a study on the ages when respondents first married. Here's the transcription: --- **7. A study asked respondents, "If ever married, how old were you when you first married?" The results are summarized in the technology excerpt that follows. Complete parts (a) through (d) below.** **One-Sample T: AGEWED** | Variable | N | Mean | StDev | SE Mean | 95.0% CI | |----------|------|-------|-------|---------|-------------------| | AGEWED | 26910| 23.370| 4.714 | 0.029 | (23.314, 23.426) | 13 Click the icon to view the table of critical t-values. (a) Use the summary to determine the point estimate of the population mean and margin of error for the confidence interval. - \( \bar{x} = \_\_\_\_\_\_\_\_\_ \) (Type an integer or a decimal. Do not round.) - \( E = \_\_\_\_\_\_\_\_\_ \) (Type an integer or a decimal. Do not round.) (b) Interpret the confidence interval. - O A. One can be 95% confident that the mean age of people when first married is 23.370 years. - O B. One can be 95% confident that the mean age of people when first married is between 23.314 and 23.426 years. - O C. There is a 95% probability that the mean age of people when first married is between 23.314 and 23.426 years. - O D. There is a 95% probability that the mean age of people when first married is 23.370 years. (c) Verify the results by computing a 95% confidence interval with the information provided. Begin with the lower bound. \[\_\_\_\_\_\_\_\_\_\_\_\_\_\_ (1) \times \_\_\_\_\_\_\_\_\_\_\_\_ \cdot 4.714 = \_\_\_\_\_\_\_\_\_\_\_\] (Round to three decimal places as needed.) Next find the upper bound. \[\_\_\_\_\_\_\_\_\_\_\_\_\_\_ (2) \times \_\_\_\_\_\_\_\_\_\
**Educational Resource: Understanding the t-Distribution Table** The provided image is a t-distribution table with the area calculated in the right tail. This statistical table is used to find critical values of the t-distribution which is commonly utilized in hypothesis testing, particularly for small sample sizes or when the population standard deviation is unknown. **Graph Description:** - There is a small graph at the top left labeled "Area in right tail," showing a typical bell curve representing the t-distribution. - The shaded region under the right tail signifies the area representing the probability or significance level. **Table Explanation:** **Header Row:** - The top row represents the area in the right tail, with various significance levels: 0.25, 0.20, 0.15, 0.10, 0.05, 0.025, 0.02, 0.01, 0.005, 0.0025, 0.001, and 0.0005. **First Column:** - This lists "Degrees of Freedom (df)," which typically equals the sample size minus one. This value is crucial in determining which row to reference for a given test. **Data Cells:** - Each cell in the table provides the critical t-value corresponding to the specific degrees of freedom and the area in the right tail. **Usage:** For statistical testing purposes, one would find the appropriate row using the degrees of freedom from their sample and select the column corresponding to the desired significance level. The intersecting cell gives the critical t-value needed to interpret results in t-tests or confidence intervals. This table is essential for students and researchers conducting t-tests, enabling them to draw inferences about population parameters based on sample data.
Transcribed Image Text:**Educational Resource: Understanding the t-Distribution Table** The provided image is a t-distribution table with the area calculated in the right tail. This statistical table is used to find critical values of the t-distribution which is commonly utilized in hypothesis testing, particularly for small sample sizes or when the population standard deviation is unknown. **Graph Description:** - There is a small graph at the top left labeled "Area in right tail," showing a typical bell curve representing the t-distribution. - The shaded region under the right tail signifies the area representing the probability or significance level. **Table Explanation:** **Header Row:** - The top row represents the area in the right tail, with various significance levels: 0.25, 0.20, 0.15, 0.10, 0.05, 0.025, 0.02, 0.01, 0.005, 0.0025, 0.001, and 0.0005. **First Column:** - This lists "Degrees of Freedom (df)," which typically equals the sample size minus one. This value is crucial in determining which row to reference for a given test. **Data Cells:** - Each cell in the table provides the critical t-value corresponding to the specific degrees of freedom and the area in the right tail. **Usage:** For statistical testing purposes, one would find the appropriate row using the degrees of freedom from their sample and select the column corresponding to the desired significance level. The intersecting cell gives the critical t-value needed to interpret results in t-tests or confidence intervals. This table is essential for students and researchers conducting t-tests, enabling them to draw inferences about population parameters based on sample data.
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