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The data table contains waiting times of customers at a bank, where customers enter a single waiting line that feeds three teller windows. Test the claim that the standard deviation of waiting times is less than 1.7 minutes, which is the standard deviation of waiting times the same bank when separate waiting lines are used each teller window. Use a significance level of 0.01. Complete parts (a) through (d) below.

The data table contains waiting times of customers at a bank, where customers enter a single waiting line that feeds three teller windows. Test the claim that the standard deviation of waiting times is less than 1.7 minutes, which is the standard deviation of waiting times the same bank when separate waiting lines are used each teller window. Use a significance level of 0.01. Complete parts (a) through (d) below.

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
Problem 1P
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The image contains a problem related to statistical hypothesis testing using waiting time data for customers at a bank. ### Problem Statement: The goal is to test the claim that the standard deviation of waiting times is less than 1.7 minutes, which is the standard deviation for separate waiting lines at each teller window. The significance level is 0.01. ### Tasks: #### a. Identify the null and alternative hypotheses: - **Options:** - **A.** \( H_0: \sigma = 1.7 \text{ minutes}; \quad H_A: \sigma < 1.7 \text{ minutes} \) - **B.** \( H_0: \sigma < 1.7 \text{ minutes}; \quad H_A: \sigma = 1.7 \text{ minutes} \) - **C.** \( H_0: \sigma = 1.7 \text{ minutes}; \quad H_A: \sigma \neq 1.7 \text{ minutes} \) - **D.** \( H_0: \sigma = 1.7 \text{ minutes}; \quad H_A: \sigma < 1.7 \text{ minutes} \) #### b. Compute the test statistic: - Compute \( \chi^2 \) statistic (Round to two decimal places). #### c. Find the P-value of the test statistic: - Determine the P-value (Round to three decimal places). #### d. Determine the conclusion: - Decide if the single line appears to reduce the variation among waiting times. - State the conclusion based on the hypothesis test results. ### Graph/Diagram Explanation: - The **Customer Waiting Times** table displays waiting times (in minutes) across several entries: ``` 8.6, 6.5, 8.9, 7.9 7.9, 7.6, 7.6, 6.3 6.4, 6.4, 6.6, 7.9 7.7, 13.9, 7.2, 8.2 8.2, 8.9, 5.8, 6.8 6.4, 6.2, 7.2, 5.2 6.9, 8.4, 7.2, 8.7 6
Transcribed Image Text:The image contains a problem related to statistical hypothesis testing using waiting time data for customers at a bank. ### Problem Statement: The goal is to test the claim that the standard deviation of waiting times is less than 1.7 minutes, which is the standard deviation for separate waiting lines at each teller window. The significance level is 0.01. ### Tasks: #### a. Identify the null and alternative hypotheses: - **Options:** - **A.** \( H_0: \sigma = 1.7 \text{ minutes}; \quad H_A: \sigma < 1.7 \text{ minutes} \) - **B.** \( H_0: \sigma < 1.7 \text{ minutes}; \quad H_A: \sigma = 1.7 \text{ minutes} \) - **C.** \( H_0: \sigma = 1.7 \text{ minutes}; \quad H_A: \sigma \neq 1.7 \text{ minutes} \) - **D.** \( H_0: \sigma = 1.7 \text{ minutes}; \quad H_A: \sigma < 1.7 \text{ minutes} \) #### b. Compute the test statistic: - Compute \( \chi^2 \) statistic (Round to two decimal places). #### c. Find the P-value of the test statistic: - Determine the P-value (Round to three decimal places). #### d. Determine the conclusion: - Decide if the single line appears to reduce the variation among waiting times. - State the conclusion based on the hypothesis test results. ### Graph/Diagram Explanation: - The **Customer Waiting Times** table displays waiting times (in minutes) across several entries: ``` 8.6, 6.5, 8.9, 7.9 7.9, 7.6, 7.6, 6.3 6.4, 6.4, 6.6, 7.9 7.7, 13.9, 7.2, 8.2 8.2, 8.9, 5.8, 6.8 6.4, 6.2, 7.2, 5.2 6.9, 8.4, 7.2, 8.7 6
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