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A simple random sample of size n is drawn. The sample mean, x, is found to be 19.3, and the sample standard deviation, s, is found to be 4.9. Click the icon to view the table of areas under the t-distribution. (a) Construct a 95% confidence interval about u if the sample size, n, is 35. Lower bound: D; Upper bound: (Use ascending order. Round to two decimal places as needed.) (b) Construct a 95% confidence interval about u if the sample size, n, is 61. Lower bound: Upper bound: (Use ascending order. Round to two decimal places as needed.) How does increasing the sample size affect the margin of error, E? O A. The margin of error decreases. O B. The margin of error increases. OC. The margin of error does not change. (c) Construct a 99% confidence interval about u if the sample size, n, is 35. Upper bound: (Use ascending order. Round to two decimal places as needed.) Lower bound: Compare the results to those obtained in part (a). How does increasing the level of confidence affect the size of the margin of error, E? O A. The margin of error does not change. OB. The margin of error decreases. OC. The margin of error increases. (d) If the sample size is 15, what conditions must be satisfied to compute the confidence interval? O A. The sample data must come from a population that is normally distributed with no outliers. O B. The sample must come from a population that is normally distributed and the sample size must be large. O C. The sample size must be large and the sample should not have any outliers.

A simple random sample of size n is drawn. The sample mean, x, is found to be 19.3, and the sample standard deviation, s, is found to be 4.9. Click the icon to view the table of areas under the t-distribution. (a) Construct a 95% confidence interval about u if the sample size, n, is 35. Lower bound: D; Upper bound: (Use ascending order. Round to two decimal places as needed.) (b) Construct a 95% confidence interval about u if the sample size, n, is 61. Lower bound: Upper bound: (Use ascending order. Round to two decimal places as needed.) How does increasing the sample size affect the margin of error, E? O A. The margin of error decreases. O B. The margin of error increases. OC. The margin of error does not change. (c) Construct a 99% confidence interval about u if the sample size, n, is 35. Upper bound: (Use ascending order. Round to two decimal places as needed.) Lower bound: Compare the results to those obtained in part (a). How does increasing the level of confidence affect the size of the margin of error, E? O A. The margin of error does not change. OB. The margin of error decreases. OC. The margin of error increases. (d) If the sample size is 15, what conditions must be satisfied to compute the confidence interval? O A. The sample data must come from a population that is normally distributed with no outliers. O B. The sample must come from a population that is normally distributed and the sample size must be large. O C. The sample size must be large and the sample should not have any outliers.

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
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# t-Distribution Table: Area in Right Tail This table provides critical t-values for a specified significance level (area in the right tail) and degrees of freedom (df) in a statistical t-distribution. These values are used to determine the cutoff points for hypothesis testing. ### Degrees of Freedom (df) Values from 1 to 100 are provided in the leftmost column, with additional values for 1000 df. ### Significance Levels The columns represent different significance levels (α) ranging from 0.25 to 0.0005. ### Table Structure Each cell contains the critical t-value corresponding to the intersection of degrees of freedom and the significance level. The table is shaded alternately by row for ease of reference. **Example Usage:** - To find the critical t-value for 10 degrees of freedom with a significance level of 0.05, locate the row for df = 10 and the column for 0.05. The critical value is 1.812. This table is a valuable resource for conducting statistical tests, including t-tests in experimental research.
Transcribed Image Text:# t-Distribution Table: Area in Right Tail This table provides critical t-values for a specified significance level (area in the right tail) and degrees of freedom (df) in a statistical t-distribution. These values are used to determine the cutoff points for hypothesis testing. ### Degrees of Freedom (df) Values from 1 to 100 are provided in the leftmost column, with additional values for 1000 df. ### Significance Levels The columns represent different significance levels (α) ranging from 0.25 to 0.0005. ### Table Structure Each cell contains the critical t-value corresponding to the intersection of degrees of freedom and the significance level. The table is shaded alternately by row for ease of reference. **Example Usage:** - To find the critical t-value for 10 degrees of freedom with a significance level of 0.05, locate the row for df = 10 and the column for 0.05. The critical value is 1.812. This table is a valuable resource for conducting statistical tests, including t-tests in experimental research.
A simple random sample of size \( n \) is drawn. The sample mean, \( \bar{x} \), is found to be 19.3, and the sample standard deviation, \( s \), is found to be 4.9. **(a)** Construct a 95% confidence interval about \( \mu \) if the sample size, \( n \), is 35. - Lower bound: \(\_\_\_\_\_\_\) ; Upper bound: \(\_\_\_\_\_\_\) *(Use ascending order. Round to two decimal places as needed.)* **(b)** Construct a 95% confidence interval about \( \mu \) if the sample size, \( n \), is 61. - Lower bound: \(\_\_\_\_\_\_\) ; Upper bound: \(\_\_\_\_\_\_\) *(Use ascending order. Round to two decimal places as needed.)* **How does increasing the sample size affect the margin of error, \( E \)?** - **A.** The margin of error decreases. - **B.** The margin of error increases. - **C.** The margin of error does not change. **(c)** Construct a 99% confidence interval about \( \mu \) if the sample size, \( n \), is 35. - Lower bound: \(\_\_\_\_\_\_\) ; Upper bound: \(\_\_\_\_\_\_\) *(Use ascending order. Round to two decimal places as needed.)* **Compare the results to those obtained in part (a). How does increasing the level of confidence affect the size of the margin of error, \( E \)?** - **A.** The margin of error does not change. - **B.** The margin of error decreases. - **C.** The margin of error increases. **(d)** If the sample size is 15, what conditions must be satisfied to compute the confidence interval? - **A.** The sample data must come from a population that is normally distributed with no outliers. - **B.** The sample must come from a population that is normally distributed and the sample size must be large. - **C.** The sample size must be large and the sample should not have any outliers.
Transcribed Image Text:A simple random sample of size \( n \) is drawn. The sample mean, \( \bar{x} \), is found to be 19.3, and the sample standard deviation, \( s \), is found to be 4.9. **(a)** Construct a 95% confidence interval about \( \mu \) if the sample size, \( n \), is 35. - Lower bound: \(\_\_\_\_\_\_\) ; Upper bound: \(\_\_\_\_\_\_\) *(Use ascending order. Round to two decimal places as needed.)* **(b)** Construct a 95% confidence interval about \( \mu \) if the sample size, \( n \), is 61. - Lower bound: \(\_\_\_\_\_\_\) ; Upper bound: \(\_\_\_\_\_\_\) *(Use ascending order. Round to two decimal places as needed.)* **How does increasing the sample size affect the margin of error, \( E \)?** - **A.** The margin of error decreases. - **B.** The margin of error increases. - **C.** The margin of error does not change. **(c)** Construct a 99% confidence interval about \( \mu \) if the sample size, \( n \), is 35. - Lower bound: \(\_\_\_\_\_\_\) ; Upper bound: \(\_\_\_\_\_\_\) *(Use ascending order. Round to two decimal places as needed.)* **Compare the results to those obtained in part (a). How does increasing the level of confidence affect the size of the margin of error, \( E \)?** - **A.** The margin of error does not change. - **B.** The margin of error decreases. - **C.** The margin of error increases. **(d)** If the sample size is 15, what conditions must be satisfied to compute the confidence interval? - **A.** The sample data must come from a population that is normally distributed with no outliers. - **B.** The sample must come from a population that is normally distributed and the sample size must be large. - **C.** The sample size must be large and the sample should not have any outliers.
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