10.1-2 4 please help thanks **Hypothesis Testing Overview:**Consider the hypothesis test \( H_0 : \mu_1 = \mu_2 \) against \( H_1 : \mu_1 \neq \mu_2 \). Suppose the sample sizes are \( n_1 = 15 \) and \( n_2 = 15 \), with sample means \( \bar{x}_1 = 4.8 \) and \( \bar{x}_2 = 7.7 \). The sample variances are \( s_1^2 = 4 \) and \( s_2^2 = 6.24 \). Assume that \( \sigma_1^2 = \sigma_2^2 \) and that the data are drawn from normal distributions. Use a significance level of \( \alpha = 0.05 \).**Tasks:**(a) **Test the Hypothesis and Find the P-Value:**Determine whether the null hypothesis should be rejected. Input the P-value in the provided field, rounding the answer to four decimal places (e.g., 98.7654).(b) **Calculate the Power for a True Difference of 3:**Calculate the power of the test from part (a) assuming a true difference in means of 3. Enter the power rounded to two decimal places (e.g., 98.76).(c) **Determine Sample Size for a True Difference of -2:**Assuming equal sample sizes, calculate the sample size needed for a power \(\beta = 0.05\) if the true difference in means is -2. Answer should be rounded to the nearest integer.**Interactive Fields and Instructions:**- For part (a), select whether the null hypothesis is rejected or not and enter the P-value.- For part (b), provide the power of the test.- For part (c), input the sample size \( n_1 = n_2 \).Reference **Statistical Tables and Charts** if required for calculations.

From the given information, The null hypothesis is,Ho:μ1=μ2 The alternative hypothesis is, H1:μ1≠μ2…

and X₂ = 7.7 and that s² = 4 and s Consider the hypothesis test Ho: ₁ = 2 against H₁: M₁ M₂. Suppose that sample sizes are n₁ = 15 and n2 = 15, that x₁ = 4.8 6.24. Assume that o? = 0 and that the data are drawn from normal distributions. Use = α = 0.05. (a) Test the hypothesis and find the P-value. (b) What is the power of the test in part (a) for a true difference in means of 3? (c) Assuming equal sample sizes, what sample size should be used to obtain ß = 0.05 if the true difference in means is -2? Assume that a = 0.05. (a) The null hypothesis rejected. The P-value is i . Round your answer to four decimal places

and X₂ = 7.7 and that s² = 4 and s Consider the hypothesis test Ho: ₁ = 2 against H₁: M₁ M₂. Suppose that sample sizes are n₁ = 15 and n2 = 15, that x₁ = 4.8 6.24. Assume that o? = 0 and that the data are drawn from normal distributions. Use = α = 0.05. (a) Test the hypothesis and find the P-value. (b) What is the power of the test in part (a) for a true difference in means of 3? (c) Assuming equal sample sizes, what sample size should be used to obtain ß = 0.05 if the true difference in means is -2? Assume that a = 0.05. (a) The null hypothesis rejected. The P-value is i . Round your answer to four decimal places

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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Question

10.1-2 4 please help thanks

**Hypothesis Testing Overview:**

Consider the hypothesis test \( H_0 : \mu_1 = \mu_2 \) against \( H_1 : \mu_1 \neq \mu_2 \). Suppose the sample sizes are \( n_1 = 15 \) and \( n_2 = 15 \), with sample means \( \bar{x}_1 = 4.8 \) and \( \bar{x}_2 = 7.7 \). The sample variances are \( s_1^2 = 4 \) and \( s_2^2 = 6.24 \). Assume that \( \sigma_1^2 = \sigma_2^2 \) and that the data are drawn from normal distributions. Use a significance level of \( \alpha = 0.05 \).

**Tasks:**

(a) **Test the Hypothesis and Find the P-Value:**

Determine whether the null hypothesis should be rejected. Input the P-value in the provided field, rounding the answer to four decimal places (e.g., 98.7654).

(b) **Calculate the Power for a True Difference of 3:**

Calculate the power of the test from part (a) assuming a true difference in means of 3. Enter the power rounded to two decimal places (e.g., 98.76).

(c) **Determine Sample Size for a True Difference of -2:**

Assuming equal sample sizes, calculate the sample size needed for a power \(\beta = 0.05\) if the true difference in means is -2. Answer should be rounded to the nearest integer.

**Interactive Fields and Instructions:**

- For part (a), select whether the null hypothesis is rejected or not and enter the P-value.
- For part (b), provide the power of the test.
- For part (c), input the sample size \( n_1 = n_2 \).

Reference **Statistical Tables and Charts** if required for calculations.

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