CASE STUDY

Bank Robberies: A Statistical Analysis

In the article "Robbing Banks"

(Significance, Vol. 9, Issue 3,

pp. 17-21) B. Reilly et al. studied several aspects of bank robberies. As these researchers state, "Robbing a bank is the staple crime of thrillers, movies and newspapers. But ... bank robbery is not all it is cracked up to be." The researchers concentrated on the factors that determine the amount of proceeds from bank robberies, and thus were able to work out both the economics of attempting one and of preventing one. In particular, the researchers revealed that the return on an average bank robbery per person per raid is modest indeed-so modest that it is not worthwhile for the banks to spend too much money on such preventative measures as fast-rising screens at tellers' windows.

The researchers obtained exclusive data from the British Bankers' Association. In one aspect of their study, they analyzed the data from a sample of 364 bank raids over a several-year period in the United Kingdom. The following table repeats a portion of Table 1 on page 19 of the article.

The case study presents summary statistics for data on bank robberies for five variables: amount stolen, number of bank staff present, number of customers present, number of bank raiders, and travel time from the bank to the nearest police station. These summary statistics were obtained by three researchers from a sample of 364 bank raids over a several-year period in the UK. For all bank raids in the UK during the years in questions:

1. Identify and interpret a point estimate for the mean (in other words, the mean) of each of the five aforementioned variables.
2. Find and interpret a 95% confidence interval for the mean amount stolen.
3. Find and interpret a 95% confidence interval for the mean amount of bank staff present at the time of robberies.
4. Find and interpret a 95% confidence interval for the mean number of customers present at the time of robberies.
5. Find and interpret a 95% confidence interval for the mean number of bank raiders.
6. Find and interpret a 95% confidence interval for the mean travel time from the nearest police station to the bank outlet.
7. This week, we learned about confidence intervals. Are there any applications from this week’s content to your major, your profession, or your interests? Please explain.

Solution: (a) Amount stolen

The point estimate of the mean is £20,330.5

Number of bank staff present

The point estimate of the mean is 5.417 bank staff

Number of customers present

The point estimate of the mean is 2.000 customers

Number of bank raiders

The point estimate of the mean is 1.637 raiders

Travel time

The point estimate of the mean is 4.557 minutes

(b) The 95% confidence interval for the mean amount stolen is

Therefore, we are 95% confident that the true mean amount stolen is contained by the interval (£14,721.11, £25,939.89)

(c) The 95% confidence interval for the mean amount stolen is

Therefore, we are 95% confident that the true mean number of staff present is contained by the interval (4.9625, 5.8715).

(d) The 95% confidence interval for the mean number of customers present at the time of robberies is

Therefore, we are 95% confident that the true mean number of customers present at the time of robberies is contained by the interval (1.6138, 2.3862).

(e) The 95% confidence interval for the mean number of bank raiders is

Therefore, we are 95% confident that the true mean number of bank raiders is contained by the interval (1.5352, 1.7388).

(f) The 95% confidence interval for the mean travel time is

Therefore, we are 95% confident that the true mean travel time is contained by the interval (4.1348, 4.9792).

(g) This week turned out to be very revealing for me, since I was able to understand that point estimates are only part of the equation, and we need interval estimates to have the full picture, because they also take into account the corresponding measures of variation.

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