Question

6. A bank with a branch located in Crown Point wants to develop an improved process for serving customers during the noon-to-lpm lunch period. Management decides to first study the waiting time of the current process. Data is collected from a random sample of 15 customer and their waiting time is recorded (in minutes) and is located in the Excel data file for this assignment under the tab CPBank. For comparative purposes, similar data is collected from a bank in Valparaiso and is stored under the tab ValpoBank a. Assuming that the population variances from both branches are equal, is there evidence that the mean waiting time is difference between the two banks? Under a 0.05 level of significance b. Determine the p-value in part a and interpret its meaning c. In addition to equal variances, what other assumption is necessary to perform the test required by part a? Do you feel this assumption is valid? Explain (prove your conclusion.) d. Construct and interpret a 95% confidence interval estimate of the difference between the population means of the two banks

Answer 1

Date: 02/10/2019 Answer а) To test the hypothesis is that the mean waiting time is difference between the CP bank and Vaplo bank at 5% significance level The null and alternative hypothesis is, The f-test statistics is, By using MINITAB, find r-test statistics with the help of the following steps: 1) 2) 3) 4) 5) hуpothesis. 6) Import the data Select the Stat and choose the Basic Statistics option Select the 2 sanple t and enter Sunınarized data Select Assune equal variances Click option button choose Confidence level, Test difference and alternative Click Ok

Two-Sample T-Test and Cl: CP, Valpo Two-sample T for CP vs Valpo N Mean StDev SE Mean CP Valpo 15 7.11 2.08 15 4.29 1.64 0.42 0.54 Difference = mu (CP) Estimate for difference: -2.828 958 CI for difference: (-4.229, -1.427) T-Test of difference 0 (vs not =): T-Value Both use Pooled StDev 1.8733 mu (Valpo) 0.000 DF 28 -4.13 P-Value From the MINITAB output, the t-test statistics is-4.13 b) The p-value for this test is, From the MINITAB output in part (a), the p-value for this test is 0.000

Decision The conclusion is that p-value in this context is less than 0.05 which is 0.000, so the null hypothesis is rejected at 5% level of significance. There is sufficient evidence to indicate that the mean waiting time is difference between the CP bank and Vaplo bank. The result is statistically significant. c) In addition to equal variances, the other assumption is necessary to perform the test required in part (a) is each sample is approximately normally distributed. The normal probability plot for CP bank and Vaplo bank data is, By using MINITAB software, draw normal probability plot with the help of following steps: 1) 2) 3) 4) 5) Import the data Select Probability Plot from the Graph Select Multiple Select Graph Variables Click Ok menu

Probability Plot of CP, Valpo Normal 95% CI 99 Variable CP Valpo 95 90 80 70 60 50 40 30 20 10 5 1 7.5 0.0 2.5 5.0 12.5 15.0 10.0 Data From the MINITAB output, the normal probability plot for CP bank and Vaplo bank data concludes the data are fall in straight line and no outlier present in the plot indicate each data is follow approximately normal distribution. It does feel that this assumption is valid Percent un

d) A 95% confidence interval estimate of the difference between the population means waiting times of CP bank and Vaplo bank is, From MINITAB output in part (a), a 95% confidence interval estimate of the difference between the population means waiting times of CP bank and Vaplo bank is - 4.23 to 1.43 Interpretation ofconfidence interval There are 95% confident that the difference between the population means waiting times of CP bank and Vaplo bank is between -4.23 and -1.43.