Essay About Sample Means T-Test And Independent Groups Assumption

The Tavern on Elm Restaurant Case Study
Problem 1:PLANObjective:  We have been hired as consultants by Randy Restaurateur to assess the effectiveness of the advertising he has been using to attract customers to one of his restaurants “The Tavern on Elm.”  Recently he has noticed a drop in sales at this particular restaurant so to combat this new issue, he has begun advertising to customers by paying $50 per advertisement each week in the Arts and Life section of the city newspaper.  We want to know if the advertisements make a positive difference in the gross weekly sales.  It is our job to analyze the statistical evidence and determine if the advertisements pay for themselves and are significant in the amount of profit that they provide.  We will find this data with a 95% confidence interval and a 5% significance test.Hypothesis:       Ho: Using the advertisement has no effect on weekly gross salesHa: Using the advertisements has an effect on the weekly gross salesAnalysis Type: Two Sample Means T-Test with pooled varianceConditions:Independence: No SRS but the data is conceivably representative of a population of interest AND the data values are conceivably independentNormal: X1 is approximately normal.[pic 1]      Figure 1: Sample 1 Data  N2 is sufficiently big.  The data from sample 2 is not normal but it is large enough that we may proceed with caution.                   [pic 2]               Figure 2: Sample 2 Data10% condition (n < 0.1N): We do not meet this condition based off of the data in the problem, but we will proceed with caution under the assumption that the number of weeks we have taken data from is less than 10% of the total weeks the restaurant has been in business. Independent Groups Assumption: This is a 2-Sample test that is independent.  We know that the different weeks in sales do not effect the other weeks in sales and therefore we meet the independent groups condition.Pooled Variance for two Independent Sample Means:  Table 1: Sample Means and Standard Deviations[pic 3]From StatCrunch, we found the standard deviation for the two samples. We calculated the variance of the two samples, and find out the ratio of two variances              [(441.33023) ^2/ (409.01004) ^2] is less than two. Hence, two independent samples pooled student T model to calculate the confident interval for the difference gross sales between During and Before the new advertising.