whats the conclusion for the last part of a whats the p value and its meaning please ### Bank Branch Waiting Time AnalysisA bank with branches in a commercial area and a residential area aims to improve customer service between noon and 1 PM. They examine waiting times by collecting data from random samples of 15 customers at each branch. Here's a detailed analysis of their findings:#### Hypotheses- **Null Hypothesis (H₀):** μ₁ = μ₂- **Alternative Hypothesis (H₁):** μ₁ ≠ μ₂#### Test Statistic- Computed t-statistic: **tₛₜₐₜ = -4.09** (rounded to two decimal places)#### Critical Values- Critical values at a chosen significance level: **-2.06, 2.05**#### Conclusion Options- **A:** Reject H₀. There is insufficient evidence that the mean waiting times differ.- **B:** Do not reject H₀. There is sufficient evidence that the mean waiting times differ.- **C:** Reject H₀. There is sufficient evidence that the mean waiting times differ.- **D:** Do not reject H₀. There is insufficient evidence that the mean waiting times differ.#### p-value- Computed p-value: **0.0001** (rounded to three decimal places)Choose the appropriate conclusion based on the test statistic and p-value.#### Interpretation Options- **1:** Probability of obtaining a sample with a t-statistic in either direction if no difference exists.- **2:** Probability of obtaining a sample with a t-statistic in the negative direction if no difference exists.- **3:** Probability of obtaining a sample with a t-statistic more extreme in either direction if no difference exists.#### Confidence Interval for Mean Difference- Construct a 95% confidence interval for population mean differences.- Computed interval: **(-1.54, -0.84)** (rounded to two decimal places)#### Confidence Interval Interpretation- **A:** Difference falls above the upper limit.- **B:** Difference lies within the interval.- **C:** Difference falls below the lower limit.- **D:** Difference lies outside the interval.#### Waiting Time Data (in minutes)- **Commercial Branch:** - 4.21, 5.66, 5.04, 3.51, 5.98, 2.67, 3.75, 4.27,

The random variable waiting time follows normal distribution. There are two independent samples…

A bank with branches located in a commercial district of a city and in a residential area has the business objective of developing an improved process for serving customers during the noon-to-1 PM. lunch period. Management decides to first study the waiting time in the current process. The waiting time is defined as the number of minutes that elapses when the customer enters the line until he or she reaches the teller window. Data are collected from a random sample of 15 customers at each branch. Complete parts (a) through (d) below m Click the icon to view the bank branch data H P2 OC. Hgi 22 D. H "2 Find the test statistic. STAT"-4.09 (Round to two decimal places as needed.) ) Find the critical value(s). <-2.05, 2.05 (Use a comma to separate answers as needed. Round to two decimal places as needed) Choose the correct conclusion below Waiting time data A. Reject Ho. There is insufficient evidence that the mean waiting time between the two branches differ. Commercial Residential 9.58 5.81 8.01 5.64 8.57 3.84 825 3 8. Do not reject Ho. There is sufficient evidence that the mean waiting time between the two branches differ. 421 5.56 3.04 5.31 4.56 2.67 OC. Reject Ho. There is sufficient evidence that the mean walting time between the two branches differ. OD. Do not reject Ha. There is insufficient evidence that the mean waiting time between the two branches differ. b. Determine the p-value in (a) and interpret its meaning 3.47 3.02 4.68 6.08 0.26 5.07 8.53 10.43 6.83 5.68 p-value O (Round to three decimal places as needed.) Interpret the p-value. Choose the correct answer below 6.35 6.48 3.58 4.13 6.01 9.82 5.38 A. Ris the probability of obtaining a sample that yields a t-test statistic farther away from 0 in either direction than the computed test statistic if there is no difference in the mean waiting time between commercial and residential banks. OB. Ris the probability of obtaining a sample that yields a t-test statistic farther away from 0 in the negative direction than the computed test statistic if there is no difference in the mean waiting time between commercial and residential banks oC. Ris the probablity the two banks have diferent population mean waiting times. OD. It is the probability of obtaining a sample that yields a t-test statistic farther away from 0 in the positive direction than the computed test statistic if there is no difference in the mean waiting time between commercial and residential banks.