help! ### Statistical Analysis of Health Insurance Costs: Washington vs Idaho Residents#### Problem Statement:You wish to test the claim that Washington residents (Group 2) have a higher average monthly bill for their health insurance than Idaho residents (Group 1) at a significance level of α = 0.02.#### Hypotheses:- Null Hypothesis (H₀): μ₁ - μ₂ = 0- Alternative Hypothesis (Hₐ): μ₁ - μ₂ < 0You believe both populations are normally distributed, but you do not know the standard deviations for either group, nor that they have the same standard deviation.#### Data Collection:- **Idaho Residents**: - Sample Size (n₁): 21 - Sample Mean (x̄₁): 87.6 - Sample Standard Deviation (s₁): 9.5- **Washington Residents**: - Sample Size (n₂): 13 - Sample Mean (x̄₂): 97.5 - Sample Standard Deviation (s₂): 10.5#### Questions:a) What is the test statistic?b) What is the p-value?c) Explain the conclusion in the context of the problem.#### Answers Explanation:a) **Test Statistic Calculation**:To find the test statistic for unequal variances, use the following formula for two-sample t-tests:\[ t = \frac{(x̄₁ - x̄₂) - (μ₁ - μ₂)}{\sqrt{\frac{s₁²}{n₁} + \frac{s₂²}{n₂}}} \]Given that μ₁ - μ₂ = 0 under the null hypothesis:\[ t = \frac{(87.6 - 97.5)}{\sqrt{\frac{9.5²}{21} + \frac{10.5²}{13}}} \]\[ t = \frac{10.1}{\sqrt{\frac{90.25}{21} + \frac{110.25}{13}}} \]\[ t = \frac{10.1}{\sqrt{4.2976 + 8.4807}} \]\[ t = \frac{10.1}{\sqrt{12.7783}} \]\[ t = \frac{10.1}{

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Description: help! ### Statistical Analysis of Health Insurance Costs: Washington vs Idaho Residents#### Problem Statement:You wish to test the claim that Washington residents (Group 2) have a higher average monthly bill for their health insurance than Idaho resi

We have given that Sample size n1=21 ,n2=13 ,xbar1=87.6,xbar2=97.5 and s1=9.5,s2=10.5 And…

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You wish to test the claim that Washington residents (Group 2) have a higher average monthly bill for their health insurance than Idaho residents (Group 1) at a significance level of a=0.02. Ho: H1 - H2 = 0 Ha: H1 – µ2 < 0 You believe both populations are normally distributed, but you do not know the standard deviations for either or that they have the same standard deviation. You obtain a sample of size 21 with a mean of 87.6 and a standard deviation of 9.5 from the Idaho residents. You obtain a sample of size 13 with a mean of 97.5 and a standard deviation of 10.5 from the Washington residents. a) What is the test statistic? b) What is the p-value? c) Explain the conclusion in the context of the problem.

You wish to test the claim that Washington residents (Group 2) have a higher average monthly bill for their health insurance than Idaho residents (Group 1) at a significance level of a=0.02. Ho: H1 - H2 = 0 Ha: H1 – µ2 < 0 You believe both populations are normally distributed, but you do not know the standard deviations for either or that they have the same standard deviation. You obtain a sample of size 21 with a mean of 87.6 and a standard deviation of 9.5 from the Idaho residents. You obtain a sample of size 13 with a mean of 97.5 and a standard deviation of 10.5 from the Washington residents. a) What is the test statistic? b) What is the p-value? c) Explain the conclusion in the context of the problem.

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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help!

### Statistical Analysis of Health Insurance Costs: Washington vs Idaho Residents

#### Problem Statement:
You wish to test the claim that Washington residents (Group 2) have a higher average monthly bill for their health insurance than Idaho residents (Group 1) at a significance level of α = 0.02.

#### Hypotheses:
- Null Hypothesis (H₀): μ₁ - μ₂ = 0
- Alternative Hypothesis (Hₐ): μ₁ - μ₂ < 0

You believe both populations are normally distributed, but you do not know the standard deviations for either group, nor that they have the same standard deviation.

#### Data Collection:
- **Idaho Residents**:
- Sample Size (n₁): 21
- Sample Mean (x̄₁): 87.6
- Sample Standard Deviation (s₁): 9.5

- **Washington Residents**:
- Sample Size (n₂): 13
- Sample Mean (x̄₂): 97.5
- Sample Standard Deviation (s₂): 10.5

#### Questions:
a) What is the test statistic?

b) What is the p-value?

c) Explain the conclusion in the context of the problem.

#### Answers Explanation:

a) **Test Statistic Calculation**:
To find the test statistic for unequal variances, use the following formula for two-sample t-tests:

\[ t = \frac{(x̄₁ - x̄₂) - (μ₁ - μ₂)}{\sqrt{\frac{s₁²}{n₁} + \frac{s₂²}{n₂}}} \]

Given that μ₁ - μ₂ = 0 under the null hypothesis:

\[ t = \frac{(87.6 - 97.5)}{\sqrt{\frac{9.5²}{21} + \frac{10.5²}{13}}} \]
\[ t = \frac{10.1}{\sqrt{\frac{90.25}{21} + \frac{110.25}{13}}} \]
\[ t = \frac{10.1}{\sqrt{4.2976 + 8.4807}} \]
\[ t = \frac{10.1}{\sqrt{12.7783}} \]
\[ t = \frac{10.1}{

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