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Data collected by a price reporting agency 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.

3.39 3.59 4.99 3.76 3.35 3.71 3.65 3.80 3.95 3.36
3.57 3.39 3.75 3.79 4.15 3.66 3.83 3.93 3.61 3.57

Required:
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.
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?

Respuesta :

anthougo

a. Based on the sample data, the mean price in dollars for a gallon of unleaded gasoline in San Francisco is $3.74.

b. The sample standard deviation in dollars is $0.37.

c. The national average price per gallon is $3.28 while the average price in San Francisco is $3.74. This means that the price per gallon is higher in San Francisco than the national average by $0.46 ($3.74 - $3.28) per gallon.

How to calculate the standard deviation

  1. Work out the Mean (the simple average of the numbers)
  2. For each number, subtract the Mean and square the result
  3. Work out the mean of those squared differences.
  4. Take the square root of the result.

Data and Calculations:

Average price of a gallon of unleaded gasoline in U.S. = $3.28

Number of gasoline and convenience stores for the U.S. average price = 90,000

Sample of San Francisco gasoline and convenience stores = 20

Prices of a gallon of gasoline in 20 San Francisco stores are as follows:

S/N.     Prices Difference in Mean  Difference Squared

1.          $3.39             -$0.35                     0.1225

2.           3.59                -0.15                     0.0225

3.           4.99                 1.25                      1.5625

4.           3.76               0.02                      0.0004

5.           3.35              -0.39                      0.1521

6.           3.71               -0.03                     0.0009

7.           3.65              -0.09                     0.0081

8.           3.80              0.06                     0.0036

9.           3.95              0.21                      0.0441

10.         3.36             -0.38                      0.1441

11.          3.57             -0.17                        0.289

12.         3.39             -0.35                      0.1225

13.         3.75              0.01                       0.0001

14.         3.79              0.05                      0.0025

15.         4.15              0.41                        0.1681

16.        3.66             -0.08                      0.0064

17.        3.83              0.09                      0.0081

18.        3.93              0.19                       0.0361

19.        3.61              -0.13                       0.0169

20.      3.57              -0.17                       0.0289

Total $74.80                                          2.7394

Mean = $3.74 ($74.80/20)                 $0.13697 ($2.27394/20)

Standard deviation = square root of $0.13697

= $0.37009 (√$0.13697)

= $0.37

Thus, in San Francisco, the price per gallon of unleaded gasoline is higher than the national average by $0.46 per gallon.

Learn more about calculating the mean and standard deviation at https://brainly.com/question/10040882

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