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Residents of Valentine, a small city in Nebraska, meet for a city council meeting once a week. Meetings are supposed to last no more than 3 hours. However, many residents are complaining that the average meeting is significantly longer than 3 hours (180 minutes). In order to test this, the lengths of the last 15 meetings were recorded in minutes: 147.0, 155.4, 159.6, 162.6, 163.8, 165.0, 167.4, 169.2, 172.2, 172.8, 172.8, 175.8, 175.8, 196.8, 201.6. Using this data, test the null hypothesis at the alpha = 0.1 level that the mean length of city council meetings is equal to 3 hours versus the alternative that the average meeting length is greater than 3 hours. Assume that the distribution of meeting lengths is normal. What is the p-value and conclusion of this test? p-value=0.046; Fail to reject the null hypothesis p-value=0.046; Reject the null hypothesis p-value = 0.990; Fail to reject the null hypothesis a

Residents of Valentine, a small city in Nebraska, meet for a city council meeting once a week. Meetings are supposed to last no more than 3 hours. However, many residents are complaining that the average meeting is significantly longer than 3 hours (180 minutes). In order to test this, the lengths of the last 15 meetings were recorded in minutes: 147.0, 155.4, 159.6, 162.6, 163.8, 165.0, 167.4, 169.2, 172.2, 172.8, 172.8, 175.8, 175.8, 196.8, 201.6. Using this data, test the null hypothesis at the alpha = 0.1 level that the mean length of city council meetings is equal to 3 hours versus the alternative that the average meeting length is greater than 3 hours. Assume that the distribution of meeting lengths is normal. What is the p-value and conclusion of this test? p-value=0.046; Fail to reject the null hypothesis p-value=0.046; Reject the null hypothesis p-value = 0.990; Fail to reject the null hypothesis a

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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### Hypothesis Testing in Civic Meetings **Context:** Residents of Valentine, a small city in Nebraska, meet for a city council meeting once a week. Meetings are supposed to last no more than 3 hours. However, many residents are complaining that the average meeting is significantly longer than 3 hours (180 minutes). **Data Collection:** To investigate this, the lengths of the last 15 meetings were recorded in minutes: - 147.0, 155.4, 159.6, 162.6, 163.8, 165.0, 167.4, 169.2, 172.2, 172.8, 172.8, 175.8, 175.8, 196.8, 201.6 **Hypothesis Testing:** Using this data, test the null hypothesis at the alpha = 0.1 level that the mean length of city council meetings is equal to 3 hours versus the alternative that the average meeting length is greater than 3 hours. Assume that the distribution of meeting lengths is normal. **Objective:** Identify the p-value and conclusion of this test based on the recorded meeting lengths. **Options:** 1. p-value = 0.046; Fail to reject the null hypothesis 2. p-value = 0.046; Reject the null hypothesis 3. p-value = 0.990; Fail to reject the null hypothesis 4. p-value = 0.990; Reject the null hypothesis **Solution Explanation:** Given the hypotheses: - Null hypothesis (H0): The mean meeting length is equal to 3 hours (180 minutes). - Alternative hypothesis (H1): The mean meeting length is greater than 3 hours. The correct option should reflect the p-value calculation and the resulting hypothesis decision: - If the p-value is less than the significance level (alpha = 0.1), we reject the null hypothesis. - If the p-value is greater than or equal to the significance level, we fail to reject the null hypothesis. Since the p-value is 0.046 and this is less than 0.1, we reject the null hypothesis. **Correct Conclusion:** **p-value = 0.046; Reject the null hypothesis** The city council meetings in Valentine indeed tend to last significantly longer than 3 hours, based on the recorded meeting lengths and statistical testing.
Transcribed Image Text:### Hypothesis Testing in Civic Meetings **Context:** Residents of Valentine, a small city in Nebraska, meet for a city council meeting once a week. Meetings are supposed to last no more than 3 hours. However, many residents are complaining that the average meeting is significantly longer than 3 hours (180 minutes). **Data Collection:** To investigate this, the lengths of the last 15 meetings were recorded in minutes: - 147.0, 155.4, 159.6, 162.6, 163.8, 165.0, 167.4, 169.2, 172.2, 172.8, 172.8, 175.8, 175.8, 196.8, 201.6 **Hypothesis Testing:** Using this data, test the null hypothesis at the alpha = 0.1 level that the mean length of city council meetings is equal to 3 hours versus the alternative that the average meeting length is greater than 3 hours. Assume that the distribution of meeting lengths is normal. **Objective:** Identify the p-value and conclusion of this test based on the recorded meeting lengths. **Options:** 1. p-value = 0.046; Fail to reject the null hypothesis 2. p-value = 0.046; Reject the null hypothesis 3. p-value = 0.990; Fail to reject the null hypothesis 4. p-value = 0.990; Reject the null hypothesis **Solution Explanation:** Given the hypotheses: - Null hypothesis (H0): The mean meeting length is equal to 3 hours (180 minutes). - Alternative hypothesis (H1): The mean meeting length is greater than 3 hours. The correct option should reflect the p-value calculation and the resulting hypothesis decision: - If the p-value is less than the significance level (alpha = 0.1), we reject the null hypothesis. - If the p-value is greater than or equal to the significance level, we fail to reject the null hypothesis. Since the p-value is 0.046 and this is less than 0.1, we reject the null hypothesis. **Correct Conclusion:** **p-value = 0.046; Reject the null hypothesis** The city council meetings in Valentine indeed tend to last significantly longer than 3 hours, based on the recorded meeting lengths and statistical testing.
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