Do students at various universities differ in how sociable they are? Twenty-five students were randomly selected from each of three universities in a region and were asked to report on the amount of time they spent socializing each day with their students. The result for University X was a mean of 5 hours and an estimated population variance of 2 hours; for University Y, ; and for University Z, What should you conclude?

Of course there is a difference! It would depend upon the size of the university/college, the curriculum a student has, even a student's temperament/personality. Even the year of study makes a difference. What would YOU conclude?

Sra

You have omitted the statistical data for Colleges Y and Z. This would be needed for a mathematical assessment of the hypothesis.

To analyze whether students at various universities differ in how sociable they are, we can compare the means and variances of the sampled students from different universities.

Given the information provided:

- For University X: The mean time spent socializing per day is 5 hours, and the estimated population variance is 2 hours.
- For University Y: The mean and variance information is not provided.
- For University Z: The mean and variance information is not provided.

Since the mean and variance for University Y and University Z are not given, we cannot draw any conclusions regarding the sociability of students at those universities.

However, based on the available information, we can conclude that, on average, students from University X spend 5 hours socializing per day, with an estimated population variance of 2 hours. This information suggests that there may be a difference in sociability among students at University X compared to the other two universities.

To further analyze and draw more robust conclusions, it would be necessary to collect data from University Y and University Z, and compare their means and variances as well.