We appreciate your visit to 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 offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
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.
Thanks for taking the time to read 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 insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
