https://r2.erweima.ai/mathbot/image/1726586932150ueqkalko.xlsx

Construyan un intervalo de confianza para determinar si el millaje recorrido por los autos fabricados por Cadillac y Chevrolet es el mismo o es diferente. Ahora, asuman que deben privilegiar la confianza sobre la exactitud. Justifiquen su elección del nivel de confianza. Asuma que las medias y las varianzas poblacionales son desconocidas.

The dataset contains millage data for Chevrolet and Cadillac vehicles. We are tasked with constructing a confidence interval to compare the means of these two brands, assuming that the population variances are unknown. Given that we should favor confidence over precision, a higher confidence level will be selected.

### Steps to follow:
1. **Formulate Hypothesis**: 
   - \( H_0 \): The mean millage for Cadillac and Chevrolet vehicles is the same.
   - \( H_a \): The mean millage for Cadillac and Chevrolet vehicles is different.

2. **Select Confidence Level**:
   - Since we are asked to prioritize confidence over exactness, a confidence level of 99% will be used.

3. **Calculate the Confidence Interval**:
   - As the population variances are unknown, we will use a **two-sample t-test** with unequal variances to calculate the confidence interval for the difference in means.

Let's proceed with these calculations.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you'd like, you can resubmit the data or try analyzing it on your own, and I can guide you step-by-step.

Here are a few related questions to help further:
1. What are some potential sources of error in comparing millage between two car brands?
2. How does increasing the confidence level affect the width of the confidence interval?
3. When is it more appropriate to prioritize confidence over precision in statistical analysis?
4. What are the key differences between a t-test and a z-test for comparing means?
5. How do we interpret a confidence interval that includes zero?

**Tip:** When variances are unknown, it's often safer to use the t-distribution rather than the z-distribution for confidence intervals.

Construct a 99% confidence interval to determine whether the mileage for Cadillac and Chevrolet cars is the same or different. This analysis involves hypothesis testing, t-distribution, and the use of a confidence interval for the difference of means with unknown variances.

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