I **Hypothesis Testing Tutorial: Testing the Average Time on Death Row****Scenario:**The state of Connecticut claims that the average time on death row is 15 years. A random survey of 75 death row inmates revealed that the average length of time on death row is 17.8 years with a standard deviation of 6 years. Conduct a hypothesis test to evaluate the state of Connecticut's claim. Use a 5% significance level.**Step-by-Step Solution:**1. **Type of Test Selection:** What type of test should be run? - $ \circ $ t-test of a mean - $ \circ $ z-test of a proportion2. **Formulating Hypotheses:** The alternative hypothesis indicates a: - $ \circ $ two-tailed test - $ \circ $ right-tailed test - $ \circ $ left-tailed test3. **Calculation and Conclusion:** Calculate the p-value. Round to 4 decimal places. $ \underline{\hspace{5cm}} $ What is the decision? - $ \circ $ We fail to reject the claim that the average time on death row is 15 years - $ \circ $ We reject the claim that the average time on death row is 15 years**Explanation:**1. **Type of Test:** To determine which test to use, note that we are dealing with sample data (75 inmates) and comparing the sample mean to a known value (15 years). Given the sample size and the nature of the data, the appropriate test is a t-test of a mean. 2. **Formulating Hypotheses:** - Null Hypothesis ($H_0$): The average time on death row is 15 years ($\mu = 15$). - Alternative Hypothesis ($H_a$): The average time on death row is not 15 years ($\mu \neq 15$). This indicates a two-tailed test since we are checking for any significant difference, whether it be greater than or less than 15 years.3. **Calculation and Conclusion:** To calculate the p-value: - We compute the test statistic ($t$) using the formula: \[ t = \frac{\bar{x} - \mu}{s / \

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Description: I **Hypothesis Testing Tutorial: Testing the Average Time on Death Row****Scenario:**The state of Connecticut claims that the average time on death row is 15 years. A random survey of 75 death row inmates revealed that the average length of time on d

The claim is that the average time on death row is 15 years.

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The state of Connecticut claims that the average time on death row is 15 years. A random survey of 75 death row inmates revealed that the average length of time on death row is 17.8 years with a standard deviation of 6 years. Conduct a hypothesis to test the state of Connecticut's claim. Use 5% significance level. What type of test should be run? t-test of a mean z-test of a proportion The alternative hypothesis indicates a two-tailed test O right-tailed test O left-tailed test Calculate the p-value. Round to 4 decimal places. What is the decision? We fail to reject the claim that the average time on death row is 15 years We reiect the clainm that the average time on death row is 15 vears

The state of Connecticut claims that the average time on death row is 15 years. A random survey of 75 death row inmates revealed that the average length of time on death row is 17.8 years with a standard deviation of 6 years. Conduct a hypothesis to test the state of Connecticut's claim. Use 5% significance level. What type of test should be run? t-test of a mean z-test of a proportion The alternative hypothesis indicates a two-tailed test O right-tailed test O left-tailed test Calculate the p-value. Round to 4 decimal places. What is the decision? We fail to reject the claim that the average time on death row is 15 years We reiect the clainm that the average time on death row is 15 vears

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

**Hypothesis Testing Tutorial: Testing the Average Time on Death Row**

**Scenario:**

The state of Connecticut claims that the average time on death row is 15 years. A random survey of 75 death row inmates revealed that the average length of time on death row is 17.8 years with a standard deviation of 6 years. Conduct a hypothesis test to evaluate the state of Connecticut's claim. Use a 5% significance level.

**Step-by-Step Solution:**

1. **Type of Test Selection:**

What type of test should be run?

- $ \circ $ t-test of a mean
- $ \circ $ z-test of a proportion

2. **Formulating Hypotheses:**

The alternative hypothesis indicates a:

- $ \circ $ two-tailed test
- $ \circ $ right-tailed test
- $ \circ $ left-tailed test

3. **Calculation and Conclusion:**

Calculate the p-value. Round to 4 decimal places. $ \underline{\hspace{5cm}} $

What is the decision?

- $ \circ $ We fail to reject the claim that the average time on death row is 15 years
- $ \circ $ We reject the claim that the average time on death row is 15 years

**Explanation:**

1. **Type of Test:**
To determine which test to use, note that we are dealing with sample data (75 inmates) and comparing the sample mean to a known value (15 years). Given the sample size and the nature of the data, the appropriate test is a t-test of a mean.

2. **Formulating Hypotheses:**
- Null Hypothesis ($H_0$): The average time on death row is 15 years ($\mu = 15$).
- Alternative Hypothesis ($H_a$): The average time on death row is not 15 years ($\mu \neq 15$).

This indicates a two-tailed test since we are checking for any significant difference, whether it be greater than or less than 15 years.

3. **Calculation and Conclusion:**
To calculate the p-value:
- We compute the test statistic ($t$) using the formula:
\[
t = \frac{\bar{x} - \mu}{s / \

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