Our Discord hit 10K members! 🎉 Meet students and ask top educators your questions.Join Here!

# One year, there were about $3,000$ institutions of higher learning in the U.S. (including junior colleges and community colleges). As part of a continuing study of higher education, the Carnegit Commission took a simple random sample of 400 of these institutions.? The average enrollment in the 400 sample schools was $3,700,$ and the SD was $6,500 .$ The Commission estimates the average enrollment at all $3,000$ institutions to be around $3,700 ;$ they put a give-or-take number of 325 on this estimate. Say whether each of the following statements is true or false, and explain. If you need more information to decide, say what you need and why.(a) An approximate 68$\%$ -confidence interval for the average enrollment of all 3, 000 institutions from $3,375$ to $4,025 .$(b) If a statistician takes a simple random sample of 400 institutions out of $3,000,$ and goes one SE either way from the average enrollment of the 400 sample schools, there is about a 68$\%$ chance that his interval will cover the average enrollment of all $3,000$ schools.(c) About 68$\%$ of the schools in the sample had enrollments in the range $3,700 \pm 6,500 .$(d) It is estimated that 68$\%$ of the $3,000$ institutions of higher learning in the U.S. enrolled between $3,700-325=3,375$ and $3,700+325=$ $4,025$ students.(e) The normal curve can't be used to figure confidence levels here at all, because the data don't follow the normal curve.

## a) true.b) true.c) false.d) true.e) false.

### Discussion

You must be signed in to discuss.