Please don't use Minitab to answer this question. ### Hypothesis Testing for Gas Prices in Minnesota#### Problem Statement:The average gas price in the US was $3.799 per gallon. A random sample of 30 gas stations in Minnesota had an average price of $3.729 with a standard deviation of $0.52. Is there enough evidence to say the average gas price in Minnesota is lower than the national average? Use $ \alpha = 0.01 $.#### Steps:1. **Identify the parameter(s)** - Mean gas price in Minnesota.2. **Null Hypothesis ($ H_0 $)** - The average gas price in Minnesota is equal to the national average: $ \mu = 3.799 $.3. **Alternative Hypothesis ($ H_a $)** - The average gas price in Minnesota is lower than the national average: $ \mu < 3.799 $.4. **Test Statistic** - Calculate the test statistic using the sample data provided.5. **Rejection Region or p-value** ![Bell Curve](https://placeholder.com/bellcurve) - A bell curve is shown indicating the rejection region at the left tail for a one-tailed test.6. **Conclusion** - Draw a conclusion based on the p-value or critical value compared to $ \alpha = 0.01 $. Determine whether to reject the null hypothesis.

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Description: Please don't use Minitab to answer this question. ### Hypothesis Testing for Gas Prices in Minnesota#### Problem Statement:The average gas price in the US was $3.799 per gallon. A random sample of 30 gas stations in Minnesota had an average price of

Given information 1) Hypothesized mean µ = $3.799 Sample size (n) = 30 gas Mean x̅ = $3.729 Standard deviation (s) = $0.52 α = 0.01 2) Hypothesis Null Hypothesis: Ho: µ = 3.799 3) Alternative Hypothesis: Ha: µ < 3.799 4) Test statistic is given by Population standard deviation is unknown, so we will use t-test Test StatisticGraph is shown belowP-value > 0.01 Conclusion Fail to reject Null Hypothesis and conclude that there is insufficient evidence to support the claim that average gas price in Minnesota is lower than the national average

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3. The average gas price in the US was $3.799 per gallon. A random sample of 30 gas stations in Minnesota had an average price of $3.729 with a standard deviation of $0.52. Is there enough evidence to say average gas price in Minnesota is lower than the national average? Use a = 0.01. 1. Identify the parameter(s) 5. Rejection Region or p-value 2. Null Hypothesis 3. Alternative Hypothesis 6. Conclusion 4. Test Statistic

3. The average gas price in the US was $3.799 per gallon. A random sample of 30 gas stations in Minnesota had an average price of $3.729 with a standard deviation of $0.52. Is there enough evidence to say average gas price in Minnesota is lower than the national average? Use a = 0.01. 1. Identify the parameter(s) 5. Rejection Region or p-value 2. Null Hypothesis 3. Alternative Hypothesis 6. Conclusion 4. Test Statistic

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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Please don't use Minitab to answer this question.

### Hypothesis Testing for Gas Prices in Minnesota

#### Problem Statement:
The average gas price in the US was $3.799 per gallon. A random sample of 30 gas stations in Minnesota had an average price of $3.729 with a standard deviation of $0.52. Is there enough evidence to say the average gas price in Minnesota is lower than the national average? Use $ \alpha = 0.01 $.

#### Steps:

1. **Identify the parameter(s)**
- Mean gas price in Minnesota.

2. **Null Hypothesis ($ H_0 $)**
- The average gas price in Minnesota is equal to the national average: $ \mu = 3.799 $.

3. **Alternative Hypothesis ($ H_a $)**
- The average gas price in Minnesota is lower than the national average: $ \mu < 3.799 $.

4. **Test Statistic**
- Calculate the test statistic using the sample data provided.

5. **Rejection Region or p-value**

![Bell Curve](https://placeholder.com/bellcurve)

- A bell curve is shown indicating the rejection region at the left tail for a one-tailed test.

6. **Conclusion**
- Draw a conclusion based on the p-value or critical value compared to $ \alpha = 0.01 $. Determine whether to reject the null hypothesis.

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