Statistical Analysis of Bank Raids: Confidence Intervals for Key Variables

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Statistical Analysis of Bank Raids: Confidence Intervals for Key Variables Variable Mean Std Deviation Amount stolen 20,330.5 53,510.2 Number of bank staff present 5,417 4,336 Number of Customers Present 2,000 3,684 Number of bank Raiders 1,637 0.971 Travel time, in minutes from Bank to nearest police station 4,557 4,028 These summary statistics were obtained by three researchers for data from a sample of 364 bank raids over a several year period in the UK. For all bank raids in the United Kingdom during the years in question: a. Identify and interpret a point estimate for the mean of each of the five aforementioned variables. Variable Point Estimate Amount stolen 20,330.5 Number of bank staff present 5,417 Number of Customers Present 2,000 Number of bank Raiders 1,637 Travel time, in minutes from Bank to nearest Police station 4,557 b. Find and interpret a 95% confidence interval for the mean amount stolen. Confidence Level (C.L.) = 95% Level of significance ( α ) = 1 - C.L. = 1 - 0.95 = 5% z α /2 = z 0.025 = 1.96 Margin of error for the mean amount stolen = z * Std. Deviation/sqrt(size) = 1.96 * 53,510.2/sqrt(364) = 5497.2 Lower Limit = 20,330.5 - 5497.2 = 14833.3 Upper Limit = 20,330.5 + 5497.2 = 25827.7
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