Thank you for visiting Listed in the accompanying table are waiting times seconds of observed cars at a Delaware inspection station The data from two waiting lines are real. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To address the problem of comparing the mean waiting times between cars in a single waiting line and those in two waiting lines, we will follow these steps:
### Step 1: Define the Hypotheses
We have been asked to determine whether the mean waiting time in a single waiting line (population 1) is equal to the mean waiting time in two waiting lines (population 2). The hypotheses are defined as follows:
- Null Hypothesis ([tex]\(H_0\)[/tex]): The means are equal, [tex]\(\mu_1 = \mu_2\)[/tex].
- Alternative Hypothesis ([tex]\(H_1\)[/tex]): The mean waiting time for the single line is greater than the mean waiting time for the two lines, [tex]\(\mu_1 > \mu_2\)[/tex].
### Step 2: Conduct a Two-Sample t-Test
Since we know that the populations are normally distributed and the population standard deviations are not assumed to be equal, a two-sample t-test for unequal variances (also known as Welch's t-test) is suitable.
### Step 3: Determine the Significance Level
The significance level ([tex]\(\alpha\)[/tex]) for the test is 0.01.
### Step 4: Analyze the Results
After conducting the t-test, we obtained the following results:
- T-statistic: Approximately 0.1595
- P-value (one-tailed): Approximately 0.4370
### Step 5: Decision Rule
In a hypothesis test, we compare the p-value to the significance level:
- If the p-value is less than [tex]\(\alpha\)[/tex] (0.01), we reject the null hypothesis.
- If the p-value is greater than or equal to [tex]\(\alpha\)[/tex], we do not reject the null hypothesis.
### Step 6: Conclusion
With a p-value of approximately 0.4370, which is much greater than the significance level of 0.01, we do not reject the null hypothesis. This indicates that we do not have enough evidence to claim that the mean waiting time in a single waiting line is greater than in two waiting lines.
Therefore, based on the data provided, we cannot conclude a significant difference in the mean waiting times between the two configurations of waiting lines at the 0.01 significance level.
### Step 1: Define the Hypotheses
We have been asked to determine whether the mean waiting time in a single waiting line (population 1) is equal to the mean waiting time in two waiting lines (population 2). The hypotheses are defined as follows:
- Null Hypothesis ([tex]\(H_0\)[/tex]): The means are equal, [tex]\(\mu_1 = \mu_2\)[/tex].
- Alternative Hypothesis ([tex]\(H_1\)[/tex]): The mean waiting time for the single line is greater than the mean waiting time for the two lines, [tex]\(\mu_1 > \mu_2\)[/tex].
### Step 2: Conduct a Two-Sample t-Test
Since we know that the populations are normally distributed and the population standard deviations are not assumed to be equal, a two-sample t-test for unequal variances (also known as Welch's t-test) is suitable.
### Step 3: Determine the Significance Level
The significance level ([tex]\(\alpha\)[/tex]) for the test is 0.01.
### Step 4: Analyze the Results
After conducting the t-test, we obtained the following results:
- T-statistic: Approximately 0.1595
- P-value (one-tailed): Approximately 0.4370
### Step 5: Decision Rule
In a hypothesis test, we compare the p-value to the significance level:
- If the p-value is less than [tex]\(\alpha\)[/tex] (0.01), we reject the null hypothesis.
- If the p-value is greater than or equal to [tex]\(\alpha\)[/tex], we do not reject the null hypothesis.
### Step 6: Conclusion
With a p-value of approximately 0.4370, which is much greater than the significance level of 0.01, we do not reject the null hypothesis. This indicates that we do not have enough evidence to claim that the mean waiting time in a single waiting line is greater than in two waiting lines.
Therefore, based on the data provided, we cannot conclude a significant difference in the mean waiting times between the two configurations of waiting lines at the 0.01 significance level.
Thank you for reading the article Listed in the accompanying table are waiting times seconds of observed cars at a Delaware inspection station The data from two waiting lines are real. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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