---### Understanding Critical t Values**Refer to the accompanying data display that results from a sample of airport data speeds in Mbps. Complete parts (a) through (c) below.**#### Step-by-Step Instructions##### a. Determining the Degrees of Freedom- **Question**: What is the number of degrees of freedom that should be used for finding the critical value \( t_{\alpha/2} \)?- **Answer**: - **Given Information for Calculation**: - Confidence Interval (\(TInterval\)): (13.046, 22.15) - Sample Mean (\(x\)): 17.598 - Sample Standard Deviation (\(S_x\)): 16.01712719 - Sample Size (\(n\)): 50 - **Calculation of Degrees of Freedom**: \[ \text{df} = n - 1 = 50 - 1 = 49 \]- **Input Field**: - df = (Type a whole number.)##### Critical t Values Explanation- **Figure**: Critical t values (right-side image) - **Graph Description**: - The figure displays two bell-shaped curves titled "Left tail" and "Right tail". - Each curve represents the distribution of t-values. - The region under the tail is shaded, indicating the critical area (\(\alpha\)). - Below each curve, there is a line marking the "Critical t value" for the tail. - **Table Description**: - The table on the right side of the figure is a "t Distribution: Critical t Values" table. - The first and last columns show the "Degrees of Freedom". - Various critical t values are listed for different levels of significance (0.01, 0.025, 0.05, 0.10) in both one-tail and two-tail scenarios.##### How to Use the Table: - Find the row corresponding to the degrees of freedom (e.g., df = 49). - Identify the critical t value by locating the appropriate column for the significance level (\(\alpha\)) of interest.> **Note**: Critical t values are essential for hypothesis testing and constructing confidence intervals. The degrees of freedom depend on the sample size, and accurate identification of df is crucial for correct analysis.---This transcription is designed to be informative for students ### Understanding Critical t-ValuesIn statistical hypothesis testing, critical t-values are significant for determining whether to reject the null hypothesis. The t-distribution, similar to the normal distribution but with heavier tails, is used when the sample size is small, and the population standard deviation is unknown. Below, we'll guide you through interpreting t-critical values based on the degrees of freedom (df) and the level of significance (\(\alpha\)).#### Graphical Representation1. **Single Tail Test (Right Tail)** - The first graph represents the critical t-value for a right-tailed test. - The area under the curve to the right of the marked t-value represents the significance level \(\alpha\). - This is used for one-tailed tests where the hypothesis predicts a direction (e.g., greater than a certain value).2. **Two-Tailed Test** - The second graph depicts a two-tailed test. - The critical region is split between two tails, each with an area of \(\alpha/2\). - This test is used when the hypothesis does not predict a direction, only that the values are different.#### Critical t-Values TableThe table below provides critical t-values corresponding to different degrees of freedom (df) and levels of significance (\(\alpha\)). Find the appropriate value by locating the df in the leftmost and rightmost columns. The intersections within the table show the critical t-values for \(\alpha\) = 0.01, 0.02, 0.05, and 0.10.| df | 0.01 | 0.02 | 0.05 | 0.10 | df ||------|-------|-------|-------|-------|------|| 18 | 2.878 | 2.552 | 2.101 | 1.734 | 18 || 19 | 2.861 | 2.539 | 2.093 | 1.729 | 19 || 20 | 2.845 | 2.528 | 2.086 | 1.725 | 20 || 21 | 2.831 | 2.518 | 2.080 | 1.721 | 21 || 22 | 2.819 | 2.508 | 2

Given: Sample size n = 50 sample mean = 17.598 sample standard deviation = 16.017127

Answered: a. What is the number of degrees of…

a. What is the number of degrees of freedom that should be used for finding the critical value tu/2? df =O (Type a whole number.) %3D

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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