Use the following data set: 40, 33, 77, 12, 23, 56, 23, 19, 29 (minutes). Assume the data is approximately bell shaped and a sample. **Problem: Hypothesis Testing****Objective:** Test the claim that $ \mu < 15 $ with a confidence level of $ c = 0.90 $.**Instructions:**1. **Sketch the Critical Value:** - To determine the critical value, identify the appropriate distribution (e.g., Z-distribution or t-distribution). Since the significance level is $ \alpha = 0.10 $ (1 - 0.90), find the critical value corresponding to the lower tail of the distribution.2. **Evaluate the Test Statistic:** - Compute the test statistic using the sample data. The formula will depend on the type of data and distribution. 3. **Determine the p-value:** - Calculate the p-value from the test statistic to understand the probability of observing a sample statistic as extreme as the test statistic, assuming that the null hypothesis is true.**Explanation:**- **Test Statistic:** This tells how far the sample statistic is from the hypothesized population parameter in standard error units.- **Critical Value:** This value separates the region where the null hypothesis is rejected from the region where it is not rejected.- **p-value:** This probability helps in making the decision. If the p-value is less than or equal to the significance level, reject the null hypothesis.**Note:** A diagram or graph associated with the distribution curve should illustrate where the critical value and test statistic fall.

h) The claim of the test is that μ<15. The hypothesis is, Null hypothesis: H0:μ≥15 Alternative…

Answered: h) Test the claim of u< 15 and use…

h) Test the claim of u< 15 and use c=.90. Provide a sketch of the Critical Value. Evaluate the Test Statistic and provide the p-value.

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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Concept explainers

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.

Question

Use the following data set: 40, 33, 77, 12, 23, 56, 23, 19, 29 (minutes). Assume the data is approximately bell shaped and a sample.

**Problem: Hypothesis Testing**

**Objective:** Test the claim that $ \mu < 15 $ with a confidence level of $ c = 0.90 $.

**Instructions:**

1. **Sketch the Critical Value:**
- To determine the critical value, identify the appropriate distribution (e.g., Z-distribution or t-distribution). Since the significance level is $ \alpha = 0.10 $ (1 - 0.90), find the critical value corresponding to the lower tail of the distribution.

2. **Evaluate the Test Statistic:**
- Compute the test statistic using the sample data. The formula will depend on the type of data and distribution.

3. **Determine the p-value:**
- Calculate the p-value from the test statistic to understand the probability of observing a sample statistic as extreme as the test statistic, assuming that the null hypothesis is true.

**Explanation:**

- **Test Statistic:** This tells how far the sample statistic is from the hypothesized population parameter in standard error units.
- **Critical Value:** This value separates the region where the null hypothesis is rejected from the region where it is not rejected.
- **p-value:** This probability helps in making the decision. If the p-value is less than or equal to the significance level, reject the null hypothesis.

**Note:** A diagram or graph associated with the distribution curve should illustrate where the critical value and test statistic fall.

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