Question

A recent survey of college graduates showed that 41.7% of all college graduates had changed their major at least once. The Margin of Error is 4.2% . We can represent this information in the form 0.417+_0.042

Express this in open interval form, for example (0.155,0.855)

Answer 1

The information given indicates that the proportion of college graduates who have changed their major at least once lies within an interval. Subtracting and adding the margin of error to the percentage provided, we get the open interval (0.375, 0.459).

Step-by-step explanation:

When we look at the statement that '41.7% of all college graduates had changed their major at least once' with a margin of error of 4.2%, we're talking about a range for the true percentage of all graduates that this survey result could represent. To express this in open interval form: Subtract 4.2% from 41.7% to find the lower bound, and add 4.2% to 41.7% to find the upper bound. This gives us an open interval.

Lower Bound = 41.7% - 4.2% = 37.5%
Upper Bound = 41.7% + 4.2% = 45.9%
So the open interval is (0.375, 0.459).