Question

The Bridgestone company is interested in analyzing the opinion of its buyers about its products. For this reason, it asks you as a consultant to carry out market research in the main cities of the country (DF, Guadalajara and Monterrey). The universe in each city is 399,987. people, the confidence level will be 95% and the estimation error is 5%. Calculate the number of surveys per city and in total.

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Andrea

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Given:

- Confidence level = 95%

- Margin of error (E) = 5%

- Population in each city = 399,987

- Number of cities = 3 (DF, Guadalajara, Monterrey)

First, we need to calculate the sample size needed per city using the sample size formula:

n = \frac{Z^2 \cdot p \cdot (1-p)}{E^2}

Since we do not have a specific estimated proportion from the population, we'll use p = 0.5 to maximize the sample size.

For a 95% confidence level, the Z-score is approximately 1.96.

Let's calculate the sample size needed per city:

n = \frac{1.96^2 \cdot 0.5 \cdot (1-0.5)}{0.05^2}

n = \frac{3.8416 \cdot 0.25}{0.0025}

n = \frac{0.9604}{0.0025}

n \approx 384.16

Rounding up, the number of surveys needed per city is 385.

Now, to find the total number of surveys needed for all three cities, we multiply the sample size by the number of cities:

Total number of surveys = 385 * 3 = 1,155.

Therefore, the company Bridgestone will need to conduct 385 surveys per city (DF, Guadalajara, Monterrey) and a total of 1,155 surveys across all three cities.

\boxed{385 \text{ surveys per city, } 1,155 \text{ surveys in total}}

- Confidence level = 95%

- Margin of error (E) = 5%

- Population in each city = 399,987

- Number of cities = 3 (DF, Guadalajara, Monterrey)

First, we need to calculate the sample size needed per city using the sample size formula:

Since we do not have a specific estimated proportion from the population, we'll use

For a 95% confidence level, the Z-score is approximately 1.96.

Let's calculate the sample size needed per city:

Rounding up, the number of surveys needed per city is 385.

Now, to find the total number of surveys needed for all three cities, we multiply the sample size by the number of cities:

Total number of surveys = 385 * 3 = 1,155.

Therefore, the company Bridgestone will need to conduct 385 surveys per city (DF, Guadalajara, Monterrey) and a total of 1,155 surveys across all three cities.

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