Math Problem Statement
Data collected by the Oil Price Information Service from more than 90,000 gasoline and convenience stores throughout the U.S. showed that the average price for a gallon of unleaded gasoline was $3.28.† The following data show the price per gallon ($) for a sample of 20 gasoline and convenience stores located in San Francisco. 3.59 3.59 4.79 3.56 3.55 3.71 3.65 3.60 3.75 3.56 3.57 3.59 3.55 3.99 4.15 3.66 3.63 3.73 3.61 3.57 (a) Use the sample data to estimate the mean price in dollars for a gallon of unleaded gasoline in San Francisco. $ (b) Compute the sample standard deviation in dollars. (Round your answer to the nearest cent.) $ (c) Compare the mean price per gallon for the sample data to the national average price. What conclusions can you draw about the cost of living in San Francisco? The average price for a gallon of unleaded gasoline in San Francisco is ---Select--- the national average. This indicates that the cost of living in San Francisco is ---Select--- it would be for cities that have an average price close to the national average.
Solution
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Math Problem Analysis
Mathematical Concepts
Descriptive Statistics
Mean
Standard Deviation
Cost Comparison
Formulas
Mean: \( \text{Mean} = \frac{\sum{X}}{n} \)
Standard Deviation: \( \sigma = \sqrt{\frac{\sum{(X - \mu)^2}}{n-1}} \)
Theorems
Central Limit Theorem
Properties of the Mean and Standard Deviation
Suitable Grade Level
Grades 9-12
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