https://file.aiquickdraw.com/mathbot/file/1730683131536mw96gkhb.jpg

To find the **p-value** for this hypothesis test, we can use the **t-test for the difference in means** (two-sample t-test), given that we're comparing the average delay times for Delta and Southwest flights. Here’s how we can approach finding the p-value step-by-step:

1. **Set up hypotheses**:
   - Null hypothesis \( H_0: \mu_1 - \mu_2 = 0 \)
   - Alternative hypothesis \( H_a: \mu_1 - \mu_2 \neq 0 \)

2. **Sample Data Summary**:
   - Mean delay for Delta flights \( \bar{x}_1 = 65.2 \)
   - Mean delay for Southwest flights \( \bar{x}_2 = 77.55 \)
   - Difference in sample means \( \bar{x}_1 - \bar{x}_2 = 65.2 - 77.55 = -12.35 \)
   - Degrees of freedom (df) = 40, as given.

3. **Calculate the Test Statistic**:
   Although the exact formula for the test statistic (t-value) requires the sample standard deviations and sample sizes for each group, let's assume the provided t-value of approximately **1.684** is correct based on the data.

4. **Determine the p-value**:
   For a two-tailed test with \( t = 1.684 \) and \( df = 40 \), you can look up this t-value in a t-distribution table or use statistical software.

   Based on common t-distribution values:
   - For \( t = 1.684 \) and \( df = 40 \), the two-tailed p-value is approximately **0.1**. This p-value is above the significance level of \( \alpha = 0.05 \), which means there isn't enough evidence to reject the null hypothesis.

5. **Conclusion**:
   Since the p-value (approximately 0.1) is greater than \( \alpha = 0.05 \), we **cannot reject the null hypothesis**. This implies there is no significant difference in the mean delay times for Delta and Southwest flights based on the sample data.

Would you like further details on any specific part of this process?

### Related Questions:
1. How would the test change if we used a one-tailed test instead of a two-tailed test?
2. How do you calculate the test statistic if you only have sample means and standard deviations?
3. What assumptions must be met to use a two-sample t-test?
4. How do degrees of freedom impact the critical value in hypothesis testing?
5. How would increasing the sample size affect the p-value?

**Tip**: When working with two-sample t-tests, ensure you understand if the test is one-tailed or two-tailed, as this impacts the p-value calculation and interpretation.

Find p-value for the hypothesis test comparing mean delay times for Delta and Southwest flights.

Learn how to perform a hypothesis test to compare the mean delay times of Delta and Southwest flights. This solution involves calculating the p-value using a two-sample t-test and interpreting the results based on a significance level of 0.05. Ideal for students in undergraduate statistics courses.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation