**Hypothesis Testing Using the p-Value Method****Scenario:**The annual per capita consumption of milk is reported to be 21.6 gallons nationwide. A sample of 16 individuals from the midwestern town of Webster City reveals a sample mean annual consumption of 24.1 gallons with a standard deviation of 4.8. The goal is to develop a hypothesis test to determine if the mean annual consumption in Webster City equals the national mean.**Step-by-Step Solution:****1. Formulate the Hypotheses:**- **Null Hypothesis (H0):** The mean annual milk consumption in Webster City is equal to the national mean. \[ H_0: \mu = 21.6 \]- **Alternative Hypothesis (H1):** The mean annual milk consumption in Webster City is not equal to the national mean. \[ H_1: \mu \neq 21.6 \]**2. Information and Calculations:**- Sample size (n): 16- Sample mean (\(\bar{x}\)): 24.1- Population mean (\(\mu\)): 21.6- Standard deviation (s): 4.8**Note:** Since \( n < 30 \), a t-test is appropriate, and we refer to the t-distribution.**3. Calculate Point Estimate:**What is the point estimate of the difference between Webster City's mean annual consumption and the national mean?\[\text{Point Estimate} = \bar{x} - \mu = 24.1 - 21.6 = 2.083\]**4. Test the Significance:**Using α = 0.05, we need to locate the critical value from the t-distribution table and compute the test statistic. Given that \( n=16 \), degrees of freedom (df) are \( n-1 = 15 \).**a. Compute the test statistic (t):**\[t = \frac{\bar{x} - \mu}{s / \sqrt{n}} = \frac{24.1 - 21.6}{4.8 / \sqrt{16}} = \frac{2.5}{1.2} \approx 2.083\]**b. Determine the p-value:**Using t-distribution tables or software for \( df = 15

Given data: Sample size = 16 Sample mean = 24.1 Population mean = 21.6 Significance level = .01…

Answered: Test the appropriate hypotheses. Use…

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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