Perform the second iteration using the updated centroids from 3.1.(i) Does any student change clusters? If no student changes clusters, the algorithm has converged — state whether it has.Converged? (Yes / No): [conv](ii) Compute the WCSS (within-cluster sum of squared Euclidean distances to the cluster centroid) of the final clustering.WCSS = [wcss]Format: enter numeric answers as plain decimals (e.g., 0.25, not 1/4). Do not include units.

A researcher conducts an independent two-sample t-test for population means using a significance level of 0.05. The test results in a p-value of 0.032. What is the correct decision?

Before training, the vendor must clean the data. (Data table is shown above.)(i) Suppose the vendor decides to impute the missing ChurroSales value of G6 using the other six recorded values (including G7). Which statistic — the mean or the median — is more appropriate here, and what is its value?Mean or median? [stat]    Imputed value: [value](ii) The vendor ultimately deletes both problematic rows (G6 and G7). Apply min-max normalization to the Attendance values of the five remaining games (G1–G5). Write the five normalized values.G1: [g1]   G2: [g2]   G3: [g3]   G4: [g4]   G5: [g5]Format: enter numeric answers as plain decimals (e.g., 0.25, not 1/4). Do not include units.

2. Game-Day Churros at Pitbull Stadium (30 points)A food vendor sells churros at FIU home football games at Pitbull Stadium. The vendor wants to predict churro sales from game attendance in order to plan inventory. The sales log for the season is below. Attendance is in thousands of fans; ChurroSales is in hundreds of churros.GameAttendance (thousands)ChurroSales (hundreds)G1128G2148G31611G41812G52011G615(missing — register crashed)G71695 (sensor glitch)

A researcher wants to compare the average patient satisfaction scores among patients treated at three different medical clinics. A One-Way ANOVA will be used. Which statement is the correct null hypothesis?

Using the five clean games (G1–G5) with the original (unnormalized) values, fit a linear regression ŷ = β0 + β1x, where x = Attendance (thousands) and y = ChurroSales (hundreds). Use the closed-form solution:β1 = Σ(xi − x̄)(yi − ȳ) / Σ(xi − x̄)² ,    β0 = ȳ − β1x̄β1 = [beta1]    β0 = [beta0]Format: enter numeric answers as plain decimals (e.g., 0.25, not 1/4). Do not include units.

A researcher conducts an independent two-sample t-test for population means to compare the average daily water consumption of adults who exercise regularly and adults who do not exercise regularly. The researcher rejects the null hypothesis. What is the correct conclusion?

A researcher wants to compare the average patient satisfaction scores among patients treated at three different medical clinics. Which hypothesis test should be used?

A researcher wants to determine whether a weight loss program is effective. Each participant’s weight is measured before starting the program and after completing the program. Which hypothesis test should be used?

A researcher conducts a one-sample t-test for a population mean and rejects the null hypothesis. What does this decision mean?