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El Concesionario de la marca “Toshiba” en Perú desea realizar una encuesta para determinar la verdadera proporción de todos los estudiantes universitarios que posee computadoras personales Toshiba. Para realizar este estudio se tomó una muestra al azar, encontrándose los siguientes resultados:

La administración de la compañía opina que el 13% de los estudiantes universitarios tienen computadoras personales marca Toshiba. A partir de los resultados, señala si es verdadera o falsa la opinión de la administración.

Seleccione una:

a. V - verdadero.


b. F - falso.

To determine whether the administration's opinion that 13% of university students own Toshiba laptops is true or false, we can analyze the given data.

### Steps:

1. **Total Number of Students in the Sample**:
   Add up the number of students for each brand to get the total number of students surveyed.
   
   \[
   \text{Total Students} = 434 (\text{HP}) + 182 (\text{Toshiba}) + 372 (\text{Dell}) + 120 (\text{ASUS}) + 205 (\text{Lenovo}) + 137 (\text{Apple})
   \]

   \[
   \text{Total Students} = 1450
   \]

2. **Proportion of Students with Toshiba Laptops**:
   Calculate the proportion of students in the sample who own Toshiba laptops.
   
   \[
   \text{Proportion} = \frac{182}{1450}
   \]

   \[
   \text{Proportion} \approx 0.1255 \text{ or } 12.55\%
   \]

3. **Comparison with the Administration's Claim**:
   The administration claims that 13% of students own Toshiba laptops. The calculated proportion from the sample is approximately 12.55%. 

   - Since 12.55% is slightly less than 13%, the difference is minimal.
   - However, strictly speaking, the sample proportion (12.55%) is less than the claimed 13%.

### Conclusion:
The opinion of the administration (that 13% of students have Toshiba laptops) is **false** based on the sample data, as the proportion is actually 12.55%.

**Answer:**
- b. F - false.

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Do you want further details or have any other questions?

### Related Questions:
1. What is the margin of error for this survey?
2. How would increasing the sample size affect the reliability of the results?
3. What statistical test could be used to formally test the administration's claim?
4. How does the proportion of Toshiba laptops compare to other brands in the sample?
5. What could be the reasons for the difference between the actual proportion and the administration's belief?

### Tip:
When conducting surveys or polls, always consider the margin of error and confidence level to determine how closely your sample results reflect the true population parameters.

Learn how to determine the true proportion of university students owning Toshiba laptops using statistical methods. Analyze survey data and compare with administrative claims. Suitable for students and professionals interested in probability and statistics.

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