Project 2 BAUD 3355 Spring 2015 Due 4/28/2015 (Tuesday) Use the \"Project 2 data\" data set. You may use Excel to help you with the statistical analysis. Abstract: A supermarket chain wants to know if their \"buy one, get one free\" campaign increases customer traffic enough to justify the cost of the program. For each of 10 stores they select two days at random to run the test. For one of those days (selected by a coin flip), the program will be in effect. They want to determine whether the program increases the mean traffic. The results in number of customer visits to the 10 stores are in the data set. Answer each of the questions below using hypothesis testing. Follow the seven-step procedure for testing a hypothesis in your text book as a guide for answering the questions. Use a .05 significance level. 1. Previous data suggests mean store traffic is 145. Is the mean traffic without the program different from 145? 2. Is the mean traffic with the program greater than 145? 3. Did the program increase store traffic? Use a pooled t-test. 4. Did the program increase store traffic? Use a paired difference t-test. Turn in your findings as described below. Generally the report will be graded for clarity (how easy it is to understand you), completeness (no significant gaps in the information provided) and correctness (the values and descriptions are correct). The report will also be graded on adherence to the report standard. The report will be structured as follows Section 1: For each question, provide The null hypothesis The alternate hypothesis The test statistic chosen (including which test) The critical value and decision rule The P-value Your findings Section 2: Questions 3 and 4 ask for two different approaches to the same question. The results differ. Write a paragraph describing which approach is the most appropriate. You should end with a clear (yes-no) conclusion to the question. 1. Previous data suggests mean store traffic is 145. Is the mean traffic without the program different from 145? 1. H: =145 Versus H: 145 Supermarket study Question 1 Store # 1 2 3 4 5 6 7 8 9 10 With Program 140 233 110 42 332 135 151 33 178 147 Without Program 136 235 108 35 328 135 144 39 170 141 Without Program Claimed Mean 136 235 108 35 328 135 144 39 170 141 145 145 145 145 145 145 145 145 145 145 t-Test: Two-Sample Assuming Unequal Variances Mean Variance Observations Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail Without Program Claimed Mean 147.1 145 7452.5444 0 10 10 0 9 0.0769 0.4702 1.8331 0.9404 2.2622 Question 2 With Program Claimed Mean 140 233 110 42 332 135 151 33 178 147 145 145 145 145 145 145 145 145 145 145 t-Test: Two-Sample Assuming Unequal Variances Mean Variance Observations Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail With Program Claimed Mean 150.1 145 7564.9889 0 10 10 0 9 0.1854 0.4285 1.8331 0.8570 2.2622 Question 3 With Program Without Program 140 233 110 42 332 135 151 33 178 147 136 235 108 35 328 135 144 39 170 141 t-Test: Two-Sample Assuming Equal Variances Mean Variance Observations Pooled Variance Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail With Program Without Program 150.1 147.1 7564.9889 7452.5444 10 10 7508.7667 0 18 0.0774 0.4696 1.7341 0.9391 2.1009 Question 4 With Program Without Program 140 233 110 42 332 135 151 33 178 147 136 235 108 35 328 135 144 39 170 141 t-Test: Paired Two Sample for Means Mean Variance Observations Pearson Correlation Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail With Program Without Program 150.1 147.1 7564.9889 7452.5444 10 10 0.9987 0 9 2.0981 0.0327 1.8331 0.0653 2.2622 Supermarket study Question 1 Store # 1 2 3 4 5 6 7 8 9 10 With Program 140 233 110 42 332 135 151 33 178 147 Without Program 136 235 108 35 328 135 144 39 170 141 Without Program Claimed Mean 136 235 108 35 328 135 144 39 170 141 145 145 145 145 145 145 145 145 145 145 t-Test: Two-Sample Assuming Unequal Variances Mean Variance Observations Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail Without Program Claimed Mean 147.1 145 7452.5444 0 10 10 0 9 0.0769 0.4702 1.8331 0.9404 2.2622 Question 2 With Program Claimed Mean 140 233 110 42 332 135 151 33 178 147 145 145 145 145 145 145 145 145 145 145 t-Test: Two-Sample Assuming Unequal Variances Mean Variance Observations Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail With Program Claimed Mean 150.1 145 7564.9889 0 10 10 0 9 0.1854 0.4285 1.8331 0.8570 2.2622 Question 3 With Program Without Program 140 233 110 42 332 135 151 33 178 147 136 235 108 35 328 135 144 39 170 141 t-Test: Two-Sample Assuming Equal Variances Mean Variance Observations Pooled Variance Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail With Program Without Program 150.1 147.1 7564.9889 7452.5444 10 10 7508.7667 0 18 0.0774 0.4696 1.7341 0.9391 2.1009 Question 4 With Program Without Program 140 233 110 42 332 135 151 33 178 147 136 235 108 35 328 135 144 39 170 141 t-Test: Paired Two Sample for Means Mean Variance Observations Pearson Correlation Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail With Program Without Program 150.1 147.1 7564.9889 7452.5444 10 10 0.9987 0 9 2.0981 0.0327 1.8331 0.0653 2.2622