help to findWhat is the P valuechoose level of significannceShould the null hypothesis be rejected?Construct a 95% confidence interval about u1-u2 Assume that both populations are normally distributed.(a) Test whether μ₁ ≠ μ₂ at the α = 0.05 level of significance for the given sample data.(b) Construct a 95% confidence interval about μ₁ - μ₂.---(a) Test whether μ₁ ≠ μ₂ at the α = 0.05 level of significance for the given sample data. Determine the null and alternative hypotheses for this test.- Option A: - H₀: μ₁ = μ₂ - H₁: μ₁ > μ₂- Option B: - H₀: μ₁ ≠ μ₂ - H₁: μ₁ is unspecified- Option C (correct): - H₀: μ₁ = μ₂ - H₁: μ₁ ≠ μ₂- Option D: - H₀: μ₁ ≠ μ₂ - H₁: μ₁ < μ₂Determine the P-value for this hypothesis test.P = ____ (Round to three decimal places as needed.)---**Data for Populations:**- **Population 1:** - n = 12 - x̄ = 14.3 - s = 2.9- **Population 2:** - n = 12 - x̄ = 16.1 - s = 3.7

(a) State the hypotheses. Obtain the value of the test statistic. From the information, given thatUse Excel to obtain the probability value. Follow the instruction to obtain the P-value: Open EXCEL Go to Formula bar. In formula bar enter the function as“=TDIST” Enter the test statistic as ABS(–1.326) Enter the degrees of freedom as 22 Enter the tails as 2. Click enter EXCEL output: From the Excel output, the P-value is 0.1984 Thus, the P-value is 0.198. Conclusion: The conclusion is obtained as shown below: Use the level of significance is 0.05. The P-value is greater than the level of significance. By rejection rule, do not reject the null hypothesis. That is, there is no evidence between the differences between two population means. (b) Obtain the 95% confidence interval for the difference between two population means. The 95% confidence interval for the difference between two population means is obtained below: The formula for two sample t-test confidence interval is, Use EXCEL Procedure for finding the critical value of t. Follow the instruction to obtain the critical value of t: Open EXCEL Go to Formula bar. In formula bar enter the function as“=TINV” Enter the probability as 0.05. Enter the degrees of freedom as 22. Click Enter. EXCEL output: From the EXCEL output, the critical value of t at the 0.05 level of significance with the 22 degrees of freedom is 2.07387 The required confidence interval is,

Math

Statistics

Population 1 Assume that both populations are normally distributed. (a) Test whetheru, #, at the a = 0.05 level of significance for the given sample data. (b) Construct a 95% confidence interval about u, -2. Population 2 12 16.1 12 14.3 2.9 3.7 (a) Test whether u, # H, at the a = 0.05 level of significance for the given sample data. Determine the null and alternative hypothesis for this test. O A. HoiH1 = H2 H >H2 O B. Ho * H2 H, >H2 c. Ho1 = 2 H,1 2 O D. HoH H2 H, 1 = H2 Detemine the P-value for this hypothesis test. P= (Round to three decimal places as needed.)

Population 1 Assume that both populations are normally distributed. (a) Test whetheru, #, at the a = 0.05 level of significance for the given sample data. (b) Construct a 95% confidence interval about u, -2. Population 2 12 16.1 12 14.3 2.9 3.7 (a) Test whether u, # H, at the a = 0.05 level of significance for the given sample data. Determine the null and alternative hypothesis for this test. O A. HoiH1 = H2 H >H2 O B. Ho * H2 H, >H2 c. Ho1 = 2 H,1 2 O D. HoH H2 H, 1 = H2 Detemine the P-value for this hypothesis test. P= (Round to three decimal places as needed.)

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

help to find

What is the P value
choose level of significannce
Should the null hypothesis be rejected?
Construct a 95% confidence interval about u1-u2

Assume that both populations are normally distributed.

(a) Test whether μ₁ ≠ μ₂ at the α = 0.05 level of significance for the given sample data.
(b) Construct a 95% confidence interval about μ₁ - μ₂.

---

(a) Test whether μ₁ ≠ μ₂ at the α = 0.05 level of significance for the given sample data. Determine the null and alternative hypotheses for this test.

- Option A:
- H₀: μ₁ = μ₂
- H₁: μ₁ > μ₂

- Option B:
- H₀: μ₁ ≠ μ₂
- H₁: μ₁ is unspecified

- Option C (correct):
- H₀: μ₁ = μ₂
- H₁: μ₁ ≠ μ₂

- Option D:
- H₀: μ₁ ≠ μ₂
- H₁: μ₁ < μ₂

Determine the P-value for this hypothesis test.

P = ____ (Round to three decimal places as needed.)

---

**Data for Populations:**

- **Population 1:**
- n = 12
- x̄ = 14.3
- s = 2.9

- **Population 2:**
- n = 12
- x̄ = 16.1
- s = 3.7

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