Final answer:
Ms. Magee's statement that the absolute value inequality '[t|4| > t > 45]' represents the range of time she spends doing research is false. The correct representation should be '|t - 43| ≤ 2' which means 41 ≤ t ≤ 45, considering the margin of error.
Step-by-step explanation:
Ms. Magee spends 43% of her working day conducting research with a margin of error of 2%. In order to represent the range of time Ms. Magee spends doing research with an absolute value inequality, we would need an inequality that accounts for this margin of error on either side of 43%. Therefore, the correct inequality should read |t - 43| ≤ 2, which gives us the solution set 41 ≤ t ≤ 45. This range shows that Ms. Magee could spend anywhere from 41% to 45% of her time doing research, taking into consideration the 2% margin of error.
The solution provided by Ms. Magee, [t|4| > t > 45], is not accurate and contains notation errors. Moreover, it doesn't correctly represent the given percentage and margin of error. Therefore, Ms. Magee's statement is false.
Understanding margins of error and absolute value inequalities is an important concept in statistics, which affects how data is interpreted. Also, a larger sample size or increased sample size can help to lower the sampling error, providing a more accurate representation of the population.