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
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7e444e2-a441-4a28-bca8-26e04764874a%2Fb4c65406-f136-48cc-a6ac-9bf55827a6a0%2Fu21gxo8_processed.jpeg&w=3840&q=75)
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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