MAT 309 CH 10 HW Example: Bank A and Bank B have each developed an improved process for serving customers. The waiting period from the moment a customer enters until he or she reaches the counter needs to be shortened. A random sample of 10 customers is selected from each bank and the results (in minutes) are shown in the accompanying data table. Complete parts (a) through(d). a) Ho : 1 2 H1 : 1 Bank A 2.23 2.22 3.69 3.01 3.03 4.09 4.61 4.14 5.72 5.52 2 Bank B 3.47 4.35 4.37 5.39 5.52 6.53 6.38 8.61 8.43 10.47 To calculate the Pooled-variance t Test for the Difference between Two means http://www.socscistatistics.com/tests/studentttest/Default2.aspx Type in Treatment 1: Bank A data; Treatment 2: Bank B data Significance Level: 0.01 Two-tailed hypothesis test Difference Scores Calculations Treatment 1 N1: 10 df1 = N - 1 = 10 - 1 = 9 M1: 3.83 SS1: 13.68 s21 = SS1(N - 1) = 13.68(10-1) = 1.52 Treatment 2 N2: 10 df2 = N - 1 = 10 - 1 = 9 M2: 6.35 SS2: 44.27 s22 = SS2(N - 1) = 44.27(10-1) = 4.92 T-value Calculation s2p = ((df1(df1 + df2)) * s21) + ((df2(df2+ df2)) * s22) = ((918) * 1.52) + ((918) * 4.92) = 3.22 s2M1 = s2pN1 = 3.2210 = 0.32 s2M2 = s2pN2 = 3.2210 = 0.32 t = (M1 - M2)(s2M1 + s2M2) = -2.530.64 = -3.15 The t-value is -3.14792. The p-value is .005564. The result is significant at p < .01. Tstat= -3.15 Find the critical values from the T-distribution table using 0.01 and 9 degrees of freedom: -2.878, 2.878 (-3.15 is < -2.878 ) Choose the correct conclusion: The T-stat is in the rejection region so we do reject the Ho which means there is sufficient evidence that the mean waiting time between the two branches differ b) Determine the p-value The p-value is .005564 This we calculated before so enter: .0055 Interpret the p-value: is 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 Bank A and Bank B. c) In addition to equal variances, what other assumption is necessary in (a)? Both sampled populations are approximately normal. d) Construct and interpret a 99% confidence interval estimate of the difference between the population means between bank A and bank B. -4.836 and -0.216 Interpret the confidence interval With 99% confidence, the difference between the population mean waiting time between the two banks falls in this interval