random sample of 280 flights from LGB to SFO using Option 1 and records their loading times. The sample mean is foun with a sample standard deviation of 4.3 minutes. They also select an independent random sample of 230 flights from LGB to SFO using C their loading times. The sample mean is found to be 18.3 minutes, with a sample standard deviation of 3.5 minutes. Since the sample siz assumed that the population standard deviation of the loading times using Option 1 and the loading times using Option 2 can be estimate standard deviation values given above. At the 0.10 level of significance, is there sufficient evidence to support the claim that the mean Op , is less than the mean Option 2 loading time, μ₂, for the airline's flights from LGB to SFO? Perform a one-tailed test. Then complete the p 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. H P Ho :D S ô H₁ :D (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) |x X 9 a 0/0 00 0=0 Oso 020 0#0 0<0 0>0
random sample of 280 flights from LGB to SFO using Option 1 and records their loading times. The sample mean is foun with a sample standard deviation of 4.3 minutes. They also select an independent random sample of 230 flights from LGB to SFO using C their loading times. The sample mean is found to be 18.3 minutes, with a sample standard deviation of 3.5 minutes. Since the sample siz assumed that the population standard deviation of the loading times using Option 1 and the loading times using Option 2 can be estimate standard deviation values given above. At the 0.10 level of significance, is there sufficient evidence to support the claim that the mean Op , is less than the mean Option 2 loading time, μ₂, for the airline's flights from LGB to SFO? Perform a one-tailed test. Then complete the p 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. H P Ho :D S ô H₁ :D (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) |x X 9 a 0/0 00 0=0 Oso 020 0#0 0<0 0>0
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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Please show all of them a,b,c,d, and e
![### Statistical Test for Mean Loading Time Difference Between Two Boarding Procedures
**Problem:** An airline is testing two new boarding procedures (Option 1 and Option 2) for flights from Long Beach (LGB) to San Francisco (SFO). Option 1 has more automation, and it is hypothesized that the mean loading time for Option 1 is less than that for Option 2. To test this hypothesis, the airline selects two random samples and records their loading times.
**Data:**
- **Option 1:**
- Sample size (n₁): 280 flights
- Sample mean (x̄₁): 17.7 minutes
- Sample standard deviation (s₁): 4.3 minutes
- **Option 2:**
- Sample size (n₂): 230 flights
- Sample mean (x̄₂): 18.3 minutes
- Sample standard deviation (s₂): 3.5 minutes
### Steps to Perform Hypothesis Testing
(a) **State the Hypotheses:**
- **Null Hypothesis (H₀):** μ₁ = μ₂ (The mean loading time for Option 1 is equal to the mean loading time for Option 2)
- **Alternative Hypothesis (H₁):** μ₁ < μ₂ (The mean loading time for Option 1 is less than the mean loading time for Option 2)
(b) **Determine the Test Statistic to Use:**
- Use a **Two-Sample t-test** for comparing the means of two independent samples.
(c) **Find the Value of the Test Statistic:**
To calculate the test statistic (t), use the formula for comparing two means:
\[ t = \frac{(x̄₁ - x̄₂)}{\sqrt{\left(\frac{s₁^2}{n₁}\right) + \left(\frac{s₂^2}{n₂}\right)}} \]
Plug in the values:
\[ t = \frac{(17.7 - 18.3)}{\sqrt{\left(\frac{4.3^2}{280}\right) + \left(\frac{3.5^2}{230}\right)}} \]
(d) **Find the Critical Value:**
- At a 0.10 level of significance (α = 0.10), determine the critical value from the t-distribution](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd1b6d45-a7eb-422c-8cfa-b963b51ff783%2Fdfe28743-c78c-4934-9e9b-bc0f5f3ca694%2F4xahwg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Statistical Test for Mean Loading Time Difference Between Two Boarding Procedures
**Problem:** An airline is testing two new boarding procedures (Option 1 and Option 2) for flights from Long Beach (LGB) to San Francisco (SFO). Option 1 has more automation, and it is hypothesized that the mean loading time for Option 1 is less than that for Option 2. To test this hypothesis, the airline selects two random samples and records their loading times.
**Data:**
- **Option 1:**
- Sample size (n₁): 280 flights
- Sample mean (x̄₁): 17.7 minutes
- Sample standard deviation (s₁): 4.3 minutes
- **Option 2:**
- Sample size (n₂): 230 flights
- Sample mean (x̄₂): 18.3 minutes
- Sample standard deviation (s₂): 3.5 minutes
### Steps to Perform Hypothesis Testing
(a) **State the Hypotheses:**
- **Null Hypothesis (H₀):** μ₁ = μ₂ (The mean loading time for Option 1 is equal to the mean loading time for Option 2)
- **Alternative Hypothesis (H₁):** μ₁ < μ₂ (The mean loading time for Option 1 is less than the mean loading time for Option 2)
(b) **Determine the Test Statistic to Use:**
- Use a **Two-Sample t-test** for comparing the means of two independent samples.
(c) **Find the Value of the Test Statistic:**
To calculate the test statistic (t), use the formula for comparing two means:
\[ t = \frac{(x̄₁ - x̄₂)}{\sqrt{\left(\frac{s₁^2}{n₁}\right) + \left(\frac{s₂^2}{n₂}\right)}} \]
Plug in the values:
\[ t = \frac{(17.7 - 18.3)}{\sqrt{\left(\frac{4.3^2}{280}\right) + \left(\frac{3.5^2}{230}\right)}} \]
(d) **Find the Critical Value:**
- At a 0.10 level of significance (α = 0.10), determine the critical value from the t-distribution
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