### 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: ______

The hypothesized mean is 2.5 hours.

Answered: The time to complete the Advanced…

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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A certain prescription medicine is supposed to contain an average of 250 parts per million (ppm) of a certain chemical. If the concentration is higher than this, the drug may cause harmful side effects; if it is lower, the drug may be ineffective. The manufacturer runs a check to see if the mean concentration in a large shipment conforms to the target level of 250 ppm or not. A simple random sample of 100 portions is tested, and the sample mean concentration is found to be 247 ppm. The sample concentration standard deviation is s = 12 ppm. What are the appropriate null and alternative hypotheses? Group of answer choices H 0: x̄ = 250 vs. H a: x̄ < 250 H 0: x̄ = 250 vs. H a: x̄ ≠ 250 H 0: x̄ = 250 vs. H a: x̄ > 250 H 0: μ = 250 vs. H a:μ < 250 H 0: μ = 250 vs. H a: μ ≠ 250 H 0: μ = 250 vs. H a: μ > 250
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A consumer advocacy group is doing a large study on car rental practices. Among other things, the consumer group would like to do a statistical test regarding the mean monthly mileage, µ, of car rented in the U.S. this year. The consumer group has reason to believe that the mean monthly mileage of cars rented in the U.S. this year is different from last year’s mean, which was 2700 miles. The group plans to do a statistical test regarding the value of µ. It chooses a random sample of monthly mileages and computes the mean of the sample to be 2565 miles and the standard deviation to be 800 miles. What are the null hypothesis (H0) and the alternative hypothesis (H1) that should be used for the test? H0: µ is ____ __? __ H1: µ is ____ __ ? ___ In the context of this test, what is a Type II error? A Type II error is ?________ ___ the hypothesis that µ is ? _____ ? when, in fact, µ is ? ____ Suppose that the group decided to reject the null…
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