An airline is trying two new boarding procedures, Option 1 and Option 2, to load passengers onto their Long Beach (LGB) to San Francisc (SFO) flights. Since Option 1 has more automation, the airline suspects that the mean Option 1 loading time is less than the mean Option loading time. To see if this is true, the airline selects a random sample of 225 flights from LGB to SFO using Option 1 and records their loading times. The sample mean is found to be 17.4 minutes, with a sample standard deviation of 4.9 minutes. They also select an independent random sample of 205 flights from LGB to SFO using Option 2 and record their loading times. The sample mean is found to 18.6 minutes, with a sample standard deviation of 4.0 minutes. Since the sample sizes are quite large, it is assumed that the population standard deviation of the loading times using Option 1 and the loading times using Option 2 can be estimated to be the sample standard deviation values given above. At the 0.01 level of significance, is there sufficient evidence to support the claim that the mean Option 1 loading time, μ₁, is less than the mean Option 2 loading time, μ₂, for the airline's flights from LGB to SFO? Perform a one-tailed test. Ther complete the parts below. Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. O Р H :D S H₁ H₁ H₂ (b) Determine the type of test statistic to use. Degrees of freedom: (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the critical value at the 0.01 level of significance. (Round to three or more decimal places.) 0 (e) Can we support the claim that the mean Option 1 loading time is less than the mean Option 2 loading time for the airline's flights from LGB to SFO? Yes No F X 4 2 0=0 OSO 020 ☐#0 >0 ? 0<0 oln X G
An airline is trying two new boarding procedures, Option 1 and Option 2, to load passengers onto their Long Beach (LGB) to San Francisc (SFO) flights. Since Option 1 has more automation, the airline suspects that the mean Option 1 loading time is less than the mean Option loading time. To see if this is true, the airline selects a random sample of 225 flights from LGB to SFO using Option 1 and records their loading times. The sample mean is found to be 17.4 minutes, with a sample standard deviation of 4.9 minutes. They also select an independent random sample of 205 flights from LGB to SFO using Option 2 and record their loading times. The sample mean is found to 18.6 minutes, with a sample standard deviation of 4.0 minutes. Since the sample sizes are quite large, it is assumed that the population standard deviation of the loading times using Option 1 and the loading times using Option 2 can be estimated to be the sample standard deviation values given above. At the 0.01 level of significance, is there sufficient evidence to support the claim that the mean Option 1 loading time, μ₁, is less than the mean Option 2 loading time, μ₂, for the airline's flights from LGB to SFO? Perform a one-tailed test. Ther complete the parts below. Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. O Р H :D S H₁ H₁ H₂ (b) Determine the type of test statistic to use. Degrees of freedom: (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the critical value at the 0.01 level of significance. (Round to three or more decimal places.) 0 (e) Can we support the claim that the mean Option 1 loading time is less than the mean Option 2 loading time for the airline's flights from LGB to SFO? Yes No F X 4 2 0=0 OSO 020 ☐#0 >0 ? 0<0 oln X G
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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Transcribed Image Text:### Airline Boarding Procedures Analysis
An airline is comparing two new boarding procedures, Option 1 and Option 2, to determine which one results in less loading time for flights from Long Beach (LGB) to San Francisco (SFO). Here’s the detailed analysis for educational purposes:
To assess the efficiency of both options, the airline collects data from a random sample of flights using each boarding procedure:
- **Option 1**:
- Sample size: 225 flights
- Sample mean loading time: 17.4 minutes
- Sample standard deviation: 4.9 minutes
- **Option 2**:
- Sample size: 205 flights
- Sample mean loading time: 18.6 minutes
- Sample standard deviation: 4.0 minutes
The objective is to test if the mean loading time of Option 1 (\( \mu_1 \)) is less than the mean loading time of Option 2 (\( \mu_2 \)).
At the 0.01 level of significance, the data is used to carry out a hypothesis test.
### Steps for Hypothesis Testing
1. **State the Hypotheses**:
- **Null Hypothesis (\( H_0 \))**: \( \mu_1 \geq \mu_2 \)
- **Alternative Hypothesis (\( H_1 \))**: \( \mu_1 < \mu_2 \)
2. **Determine the Type of Test Statistic**:
- Use the *t-test* statistic for comparison.
3. **Calculate the Test Statistic**:
- The test statistic is calculated using the formulas for the means and standard deviations of two independent samples.
4. **Find the Critical Value**:
- Determine the critical value at a 0.01 level of significance for the t-test.
5. **Decision Rule**:
- Based on the test statistic and the critical value, decide if we can reject the null hypothesis or not.
### Hypothesis Test Results
(a) **State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \)**:
\( H_0 : \mu_1 \geq \mu_2 \)
\( H_1 : \mu_1 < \mu_2 \)
(b) **Type of Test Statistic to Use**:
- Use the *t* test for comparing the
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