You are interested in finding a 90% confidence interval for the average commute that non- residential students have to their college. The data below show the number of commute miles for 15 randomly selected non-residential college students. Round answers to 3 decimal places where possible. 28 10 21 10 28 18 21 16 21 19 20 22 14 11 13 a. To compute the confidence interval use at distribution. b. With 90% confidence the population mean commute for non-residential college students is

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Please solve question b.
## Understanding Confidence Intervals for Commute Miles

### Context
In this exercise, we are interested in finding a 90% confidence interval for the average commute that non-residential students have to their college. The data below illustrates the number of commute miles for 15 randomly selected non-residential college students. All answers should be rounded to 3 decimal places.

### Data
The commute distances (in miles) for the students are as follows:

- 28, 10, 21, 10, 28, 18, 21, 16, 21, 19, 20, 22, 14, 11, 13

### Instructions and Interpretation

#### a. Distribution
To compute the confidence interval, use a t-distribution.

#### b. Calculating Confidence Interval
With 90% confidence, the mean commute for non-residential college students falls between the range indicated by the placeholders (boxes) for miles.

#### c. Understanding the Confidence Level
If multiple groups of 15 randomly selected non-residential college students are surveyed, different confidence intervals would result from each group. Approximately 90% of these intervals will contain the true population mean number of commute miles, while about 10% will not.

Through this exercise, students learn to apply statistical methodologies to real-world data, enhancing their understanding of confidence intervals and their practical implications.
Transcribed Image Text:## Understanding Confidence Intervals for Commute Miles ### Context In this exercise, we are interested in finding a 90% confidence interval for the average commute that non-residential students have to their college. The data below illustrates the number of commute miles for 15 randomly selected non-residential college students. All answers should be rounded to 3 decimal places. ### Data The commute distances (in miles) for the students are as follows: - 28, 10, 21, 10, 28, 18, 21, 16, 21, 19, 20, 22, 14, 11, 13 ### Instructions and Interpretation #### a. Distribution To compute the confidence interval, use a t-distribution. #### b. Calculating Confidence Interval With 90% confidence, the mean commute for non-residential college students falls between the range indicated by the placeholders (boxes) for miles. #### c. Understanding the Confidence Level If multiple groups of 15 randomly selected non-residential college students are surveyed, different confidence intervals would result from each group. Approximately 90% of these intervals will contain the true population mean number of commute miles, while about 10% will not. Through this exercise, students learn to apply statistical methodologies to real-world data, enhancing their understanding of confidence intervals and their practical implications.
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