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Determine the critical value(s) for a left-tailed hypothesis test for a mean with the given characteristics. Round any z-value solution to two decimal places. Round any t-value solution to four decimal places. • The significance level of the test is 1% • The sample size is 69 • The population standard deviation (o) is not known Should the tor z distribution be used for the above scenario? The Student's t distribution should be used The standard normal (2) distribution should be used = -2.6501 The critical value(s) for the test are given by tv X

Determine the critical value(s) for a left-tailed hypothesis test for a mean with the given characteristics. Round any z-value solution to two decimal places. Round any t-value solution to four decimal places. • The significance level of the test is 1% • The sample size is 69 • The population standard deviation (o) is not known Should the tor z distribution be used for the above scenario? The Student's t distribution should be used The standard normal (2) distribution should be used = -2.6501 The critical value(s) for the test are given by tv X

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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### Determining the Critical Value(s) for a Left-Tailed Hypothesis Test In this section, we will guide you through the process of determining the critical value(s) for a left-tailed hypothesis test for a mean with the given characteristics. #### Given Characteristics: - **Significance Level**: 1% - **Sample Size**: 69 - **Population Standard Deviation (σ)**: Not known #### Step-by-Step Solution: 1. **Choose the Appropriate Distribution:** - Since the population standard deviation (σ) is not known and the sample size is relatively small (<100), the appropriate distribution to use is the **Student's t distribution**. 2. **Identify the Distribution to Use:** - **Student's t distribution should be used.** - This decision is based on the criteria that we don't know the population standard deviation, and the sample size (69) isn't considered large enough to use the standard normal (z) distribution. 3. **Determine the Critical Value:** - Using the t-distribution table, technology, or statistical software, find the critical value based on the given significance level of 1% (0.01) and degrees of freedom (df = sample size - 1 = 68). - The correct calculation yields a critical t-value for this left-tailed test, which is **-2.6501**, rounded to four decimal places. #### Diagram Explanation: - In the image provided, there is an interactive section where users can input and verify their answers: - Users are first asked to select between "The Student's t distribution" and "The standard normal (z) distribution." - After selection, they need to input the corresponding critical value for the test. #### Summary: - Given the criteria where the population standard deviation is unknown and the sample size, the **Student's t distribution** is applied. - The critical t-value calculated for a left-tailed test at a 1% significance level with 68 degrees of freedom is **-2.6501**. This approach ensures you understand the conditions under which different statistical distributions are used and how to determine critical values appropriately.
Transcribed Image Text:### Determining the Critical Value(s) for a Left-Tailed Hypothesis Test In this section, we will guide you through the process of determining the critical value(s) for a left-tailed hypothesis test for a mean with the given characteristics. #### Given Characteristics: - **Significance Level**: 1% - **Sample Size**: 69 - **Population Standard Deviation (σ)**: Not known #### Step-by-Step Solution: 1. **Choose the Appropriate Distribution:** - Since the population standard deviation (σ) is not known and the sample size is relatively small (<100), the appropriate distribution to use is the **Student's t distribution**. 2. **Identify the Distribution to Use:** - **Student's t distribution should be used.** - This decision is based on the criteria that we don't know the population standard deviation, and the sample size (69) isn't considered large enough to use the standard normal (z) distribution. 3. **Determine the Critical Value:** - Using the t-distribution table, technology, or statistical software, find the critical value based on the given significance level of 1% (0.01) and degrees of freedom (df = sample size - 1 = 68). - The correct calculation yields a critical t-value for this left-tailed test, which is **-2.6501**, rounded to four decimal places. #### Diagram Explanation: - In the image provided, there is an interactive section where users can input and verify their answers: - Users are first asked to select between "The Student's t distribution" and "The standard normal (z) distribution." - After selection, they need to input the corresponding critical value for the test. #### Summary: - Given the criteria where the population standard deviation is unknown and the sample size, the **Student's t distribution** is applied. - The critical t-value calculated for a left-tailed test at a 1% significance level with 68 degrees of freedom is **-2.6501**. This approach ensures you understand the conditions under which different statistical distributions are used and how to determine critical values appropriately.
### Statistical Hypothesis Testing - P-Value Calculation In this educational example, we are determining the p-value for a two-tailed hypothesis test for different test statistics and sample sizes. --- #### Example 1: - **Test Statistic**: 1.7368 - **Sample Size**: 109 **Question**: Find the p-value for this two-tailed test of hypothesis for a mean. **Options**: - \(\ p \text{-value} < 0.001 \) - \(\ 0.001 < \ p \text{-value} < 0.01 \) - \(\ 0.01 < \ p \text{-value} < 0.02 \) - \(\ 0.02 < \ p \text{-value} < 0.05 \) *(Selected)* - \(\ 0.05 < \ p \text{-value} < 0.10 \) - \(\ 0.10 < \ p \text{-value} < 0.20 \) - \(\ p \text{-value} > 0.20 \) **Explanation**: For a test statistic of 1.7368 and a sample size of 109, the correct range for the p-value is \(0.02 < p \text{-value} < 0.05\). --- #### Example 2: - **Test Statistic**: -2.0735 - **Sample Size**: 23 **Question**: Find the p-value for this two-tailed test of hypothesis for a mean. **Options**: - \(\ p \text{-value} < 0.001 \) - \(\ 0.001 < \ p \text{-value} < 0.01 \) - \(\ 0.01 < \ p \text{-value} < 0.02 \) *(Selected)* - \(\ 0.02 < \ p \text{-value} < 0.05 \) - \(\ 0.05 < \ p \text{-value} < 0.10 \) - \(\ 0.10 < \ p \text{-value} < 0.20 \) - \(\ p \text{-value} > 0.20 \) **Explanation**: For a test statistic of -2.0735 and a sample size of
Transcribed Image Text:### Statistical Hypothesis Testing - P-Value Calculation In this educational example, we are determining the p-value for a two-tailed hypothesis test for different test statistics and sample sizes. --- #### Example 1: - **Test Statistic**: 1.7368 - **Sample Size**: 109 **Question**: Find the p-value for this two-tailed test of hypothesis for a mean. **Options**: - \(\ p \text{-value} < 0.001 \) - \(\ 0.001 < \ p \text{-value} < 0.01 \) - \(\ 0.01 < \ p \text{-value} < 0.02 \) - \(\ 0.02 < \ p \text{-value} < 0.05 \) *(Selected)* - \(\ 0.05 < \ p \text{-value} < 0.10 \) - \(\ 0.10 < \ p \text{-value} < 0.20 \) - \(\ p \text{-value} > 0.20 \) **Explanation**: For a test statistic of 1.7368 and a sample size of 109, the correct range for the p-value is \(0.02 < p \text{-value} < 0.05\). --- #### Example 2: - **Test Statistic**: -2.0735 - **Sample Size**: 23 **Question**: Find the p-value for this two-tailed test of hypothesis for a mean. **Options**: - \(\ p \text{-value} < 0.001 \) - \(\ 0.001 < \ p \text{-value} < 0.01 \) - \(\ 0.01 < \ p \text{-value} < 0.02 \) *(Selected)* - \(\ 0.02 < \ p \text{-value} < 0.05 \) - \(\ 0.05 < \ p \text{-value} < 0.10 \) - \(\ 0.10 < \ p \text{-value} < 0.20 \) - \(\ p \text{-value} > 0.20 \) **Explanation**: For a test statistic of -2.0735 and a sample size of
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