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

Given that Alpha =0.10 And n1=280 n2=230

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