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Cappuccino In San Francisco

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To determine just how expensive a cappuccino was in San Francisco, I sampled cappuccino prices at 36 coffee shops scattered across San Francisco. The sample mean price of a cappuccino is $3.54 (x̅) with a sample standard deviation, or a standard error, of $0.55 (s). The prices ranged from $2.50 to $4.40. To construct a 99% confidence interval for this sample, I multiplied the standard error by the z-statistic corresponding with 99%, 2.576, and added/subtracted that value from the point estimate, $3.54. The resultant confidence interval was [$2.13, $4.96]. In other words, if I continued sampling cappuccino coffee prices and creating unique samples of sufficient size, both including and not including the coffee shops already sampled, 99% of the…show more content…
It is possible, albeit unlikely, that the prices shown on these cafe’s websites is different from the prices they actually sell cappuccinos at. I also failed to correct for inconsistencies in cappuccino prices. Cappuccino sizes are not standardized, so I tried to pick the smallest size whenever possible, which varied from “Small” at most cafes to “Tall” at Starbucks to “12 oz” at other institutions. In order to provide a basis for equal comparison, I should have ensured that the cappuccinos in the population had the same price in liquid ounces. Additionally, some coffee shops such as Starbucks include tax in the prices listed on their menus, whereas others do not. The combined effect of the methodological problems and sampling biases leads me to conclude that my sample is most likely biased. Since confidence intervals are usually centered around sample means, which are supposed to be equal to the population means, there is evidence to believe that the constructed confidence interval contains the population mean despite the fact that it is most likely biased. First of all, the coffee shops I sampled are quite representative of San Francisco coffee shops by general price. Most of the coffee shops sampled were within the inexpensive to moderate price range as described by Yelp, which is quite representative of coffee shop prices in San
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