Question

1. -/12.5 points 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 4.59 3.56 3.55 3.91 3.65 3.40 3.55 3.76 3.37 3.79 3.55 3.99 3.95 3.86 3.43 3.53 3.41 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.

Explanation:

Step1: Sum all sample prices

First, list all 20 prices: 3.39, 3.59, 4.59, 3.56, 3.55, 3.91, 3.65, 3.40, 3.55, 3.76, 3.37, 3.79, 3.55, 3.99, 3.95, 3.86, 3.43, 3.53, 3.41, 3.57
Calculate the sum:
$$3.39+3.59+4.59+3.56+3.55+3.91+3.65+3.40+3.55+3.76+3.37+3.79+3.55+3.99+3.95+3.86+3.43+3.53+3.41+3.57 = 72.98$$

Step2: Calculate sample mean

Divide total sum by sample size $n=20$.
$$\bar{x} = \frac{72.98}{20} = 3.649 \approx 3.65$$

Step3: Compute squared deviations

Find $(x_i - \bar{x})^2$ for each data point, sum them up:
$$\sum_{i=1}^{20} (x_i - 3.649)^2 = (3.39-3.649)^2 + (3.59-3.649)^2 + ... + (3.57-3.649)^2 = 1.28258$$

Step4: Calculate sample standard deviation

Use sample standard deviation formula $s = \sqrt{\frac{\sum(x_i-\bar{x})^2}{n-1}}$.
$$s = \sqrt{\frac{1.28258}{20-1}} = \sqrt{\frac{1.28258}{19}} \approx \sqrt{0.067504} \approx 0.26$$

The sample mean price in San Francisco is compared to the national average of $\$3.28$. Since $3.65 > 3.28$, the average price in San Francisco is higher than the national average. This indicates the cost of living in San Francisco is higher than it would be for cities near the national average.

Answer:

(a) $\$3.65$
(b) $\$0.26$
(c)