### Statistical Analysis of Two Populations**Assume that both populations are normally distributed.**#### Task Breakdown:**a) Test whether $ \mu_1 > \mu_2 $ at the $ \alpha = 0.10 $ level of significance for the given sample data.****b) Construct a 90% confidence interval about $ \mu_1 - \mu_2 $.**#### Sample Data:- **Sample 1:** - $ n = 27 $ - $ \bar{x} = 53 $ - $ s = 9.7 $ - **Sample 2:** - $ n = 20 $ - $ \bar{x} = 45.2 $ - $ s = 12.3 $**Steps:**1. **Click the icon to view the Student's t-distribution table.**2. **a) Perform a hypothesis test. Determine the null and alternative hypotheses.** - Select the correct hypothesis pair from the options: - $ \text{A. } H_0: \mu_1 < \mu_2; \, H_1: \mu_1 > \mu_2 $ - $ \text{B. } H_0: \mu_1 \leq \mu_2; \, H_1: \mu_1 > \mu_2 $ [Typically the correct option for a one-tailed test] - $ \text{C. } H_0: \mu_1 = \mu_2; \, H_1: \mu_1 \neq \mu_2 $ - $ \text{D. } H_0: \mu_1 \geq \mu_2; \, H_1: \mu_1 < \mu_2 $3. **Determine the test statistic:** - Calculate $ t $ (Round to two decimal places as needed.)4. **Approximate the P-value.** - Choose the correct answer from the given intervals: - $ \text{A. P-value < 0.01} $ - $ \text{B. 0.01} \leq \text{P-value} < 0.05 $ - \( \text{C. ### t-Distribution Table#### DescriptionThe t-distribution table is used in statistics to determine critical values of the t-distribution. This table is vital for conducting hypothesis tests and calculating confidence intervals when dealing with small sample sizes, typically when the sample size is less than 30.#### Graphical RepresentationAt the top left corner of the table, there is a graphical representation of the t-distribution. The bell-shaped curve represents the general form of the t-distribution. The shaded area under the curve to the right is labeled "Area in right tail," indicating the proportion of the distribution that lies to the right of a specified t-value. This area in the right tail is crucial in hypothesis testing, especially when determining critical values.#### Table ExplanationThe table below the graph provides the critical values of the t-distribution for different degrees of freedom (df) and right-tail areas. Key components of the table include:- **Degrees of Freedom**: Represented in the first column on the left side of the table. Degrees of freedom generally account for sample size and are calculated as the sample size minus one (n-1).- **Area in Right Tail**: Each remaining column represents a different tail area (α) in the right tail of the distribution (0.25, 0.20, 0.15, 0.10, 0.05, 0.025, 0.02, 0.01, 0.005, 0.0025, 0.001, 0.0005). For example:- For 1 degree of freedom with an area of 0.10 in the right tail, the critical value is 3.078.- For 10 degrees of freedom with an area of 0.01 in the right tail, the critical value is 2.764.The t-values decrease as the degrees of freedom increase, reflecting the t-distribution approaching a normal distribution as the sample size grows.Below is a detailed transcription of the table.#### t-Distribution Critical Values```Degrees of Freedom | 0.25 | 0.20 | 0.15 | 0.10 | 0.05 | 0.025 | 0.02 | 0.01 | 0.005 | 0.0025 | 0.001 | 0.0005

Name: ### Statistical Analysis of Two Populations**Assume that both populat
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Description: ### Statistical Analysis of Two Populations**Assume that both populations are normally distributed.**#### Task Breakdown:**a) Test whether $ \mu_1 > \mu_2 $ at the $ \alpha = 0.10 $ level of significance for the given sample data.****b) Construc

We have given that Sample sizes n1=27, n2=20 xbar1=53,xbar2=45.2 and s1=9.7 ,s2=12.3 alpha=0.10…

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Statistics

ssume that both populations are normally distributed. ) Test whether u, > H, at the a = 0.10 level of significance for the given sample data. ) Construct a 90% confidence interval about p, - H2 Sample 1 27 Sample 2 20 X 53 45.2 9.7 12.3 Click the icon to view the Student's t-distribution table. ) Perform a hypothesis test. Determine the null and alternative hypotheses. DA. Ho: H1 < H2, HqH1> H2 OB. Ho H1 > H2, HHqH2 etermine the test statistic. = (Round to two decimal places as needed.) pproximate the P-value. Choose the correct answer below. OA. P-value < 0.01 OB. 0.01 sP-value < 0.05 OC. 0.05 sP-value <0.10 OD. P-value 0.10 hould the hypothesis be rejected at the a = 0.10 level of significance? the null hypothesis because the P-value is v the level of significance. ) The confidence interval is the range from to. Round to two decimal places as needed. Use ascending order.)

ssume that both populations are normally distributed. ) Test whether u, > H, at the a = 0.10 level of significance for the given sample data. ) Construct a 90% confidence interval about p, - H2 Sample 1 27 Sample 2 20 X 53 45.2 9.7 12.3 Click the icon to view the Student's t-distribution table. ) Perform a hypothesis test. Determine the null and alternative hypotheses. DA. Ho: H1 < H2, HqH1> H2 OB. Ho H1 > H2, HHqH2 etermine the test statistic. = (Round to two decimal places as needed.) pproximate the P-value. Choose the correct answer below. OA. P-value < 0.01 OB. 0.01 sP-value < 0.05 OC. 0.05 sP-value <0.10 OD. P-value 0.10 hould the hypothesis be rejected at the a = 0.10 level of significance? the null hypothesis because the P-value is v the level of significance. ) The confidence interval is the range from to. Round to two decimal places as needed. Use ascending order.)

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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