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The time to complete the Advanced Placement (AP) Statistics Exam in previous years is normally distributed with an average time of 2.5 hours. Because of school closures due to COVID-19, the College Board offered an at-home test for the 2020 AP Statistics Exam. A teacher feels that students, on average, will have a different completion time for the at-home exam. They take a random sample of 27 students that took the exam and their mean time was 2.66 hours with a standard deviation of 0.3 hours. Test to see if the mean time has significantly changed using a 5% level of significance. Give answers to at least 4 decimal places.

The time to complete the Advanced Placement (AP) Statistics Exam in previous years is normally distributed with an average time of 2.5 hours. Because of school closures due to COVID-19, the College Board offered an at-home test for the 2020 AP Statistics Exam. A teacher feels that students, on average, will have a different completion time for the at-home exam. They take a random sample of 27 students that took the exam and their mean time was 2.66 hours with a standard deviation of 0.3 hours. Test to see if the mean time has significantly changed using a 5% level of significance. Give answers to at least 4 decimal places.

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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### Instructions for Shading a Sampling Distribution Curve **Objective:** Shade the sampling distribution curve with the correct critical value(s) and identify the critical regions. **Instructions:** - **Adjusting the Arrows:** Drag the arrows to the t-scores that are accurate to one decimal place. These values correspond to the tick marks on the horizontal axis. - **Shading Options:** Use the drop-down menu to choose how to shade the area: - Shade to the left of a t-score - Shade to the right - Shade between two t-scores - **Graph Details:** The graph displays a standard normal distribution curve. The shaded area is blue, starting at t-score -4 and shading up to -1. This represents the area of interest or critical region. **Graph Components:** - **Horizontal Axis:** Ranges from -4 to 4, marked at increments that support precise adjustments. - **Vertical Axis:** Represents the probability density. - **Shaded Area:** The blue shaded area is to the left of t-score -1.0, highlighting a critical region. **Decision and Summary Section:** - **Correct Decision Dropdown:** Select whether to reject or fail to reject the null hypothesis. - **Correct Summary Dropdown:** Select whether there is sufficient evidence to conclude that the population mean time to complete the SAT has significantly changed from 2.5 hours. These tools allow for an interactive approach to understanding statistical significance and hypothesis testing.
Transcribed Image Text:### Instructions for Shading a Sampling Distribution Curve **Objective:** Shade the sampling distribution curve with the correct critical value(s) and identify the critical regions. **Instructions:** - **Adjusting the Arrows:** Drag the arrows to the t-scores that are accurate to one decimal place. These values correspond to the tick marks on the horizontal axis. - **Shading Options:** Use the drop-down menu to choose how to shade the area: - Shade to the left of a t-score - Shade to the right - Shade between two t-scores - **Graph Details:** The graph displays a standard normal distribution curve. The shaded area is blue, starting at t-score -4 and shading up to -1. This represents the area of interest or critical region. **Graph Components:** - **Horizontal Axis:** Ranges from -4 to 4, marked at increments that support precise adjustments. - **Vertical Axis:** Represents the probability density. - **Shaded Area:** The blue shaded area is to the left of t-score -1.0, highlighting a critical region. **Decision and Summary Section:** - **Correct Decision Dropdown:** Select whether to reject or fail to reject the null hypothesis. - **Correct Summary Dropdown:** Select whether there is sufficient evidence to conclude that the population mean time to complete the SAT has significantly changed from 2.5 hours. These tools allow for an interactive approach to understanding statistical significance and hypothesis testing.
The time to complete the Advanced Placement (AP) Statistics Exam in previous years is normally distributed with an average time of 2.5 hours. Because of school closures due to COVID-19, the College Board offered an at-home test for the 2020 AP Statistics Exam. A teacher feels that students, on average, will have a different completion time for the at-home exam. They take a random sample of 27 students that took the exam and their mean time was 2.66 hours with a standard deviation of 0.3 hours. Test to see if the mean time has significantly changed using a 5% level of significance. Give answers to at least 4 decimal places. **What are the correct hypotheses?** - **H₀ (Null Hypothesis):** - Select an answer: (e.g., equals, not equal to) - Enter value: 2.5 hours - **H₁ (Alternative Hypothesis):** - Select an answer: (e.g., not equal to, greater than, less than) - Enter value: 2.5 hours **Based on the hypotheses, find the following:** - **Test Statistic t =** - Enter value: ______ - **Critical-Value t = ±** - Enter value: ______
Transcribed Image Text:The time to complete the Advanced Placement (AP) Statistics Exam in previous years is normally distributed with an average time of 2.5 hours. Because of school closures due to COVID-19, the College Board offered an at-home test for the 2020 AP Statistics Exam. A teacher feels that students, on average, will have a different completion time for the at-home exam. They take a random sample of 27 students that took the exam and their mean time was 2.66 hours with a standard deviation of 0.3 hours. Test to see if the mean time has significantly changed using a 5% level of significance. Give answers to at least 4 decimal places. **What are the correct hypotheses?** - **H₀ (Null Hypothesis):** - Select an answer: (e.g., equals, not equal to) - Enter value: 2.5 hours - **H₁ (Alternative Hypothesis):** - Select an answer: (e.g., not equal to, greater than, less than) - Enter value: 2.5 hours **Based on the hypotheses, find the following:** - **Test Statistic t =** - Enter value: ______ - **Critical-Value t = ±** - Enter value: ______
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