Question 1 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
A teacher would like to estimate the mean number of steps students take during the school day. To do so, she selects a random sample of 50 students and gives each one a pedometer at the beginning of the school day. They wear the pedometers all day and then return them to her at the end of the school day. From this, she computes the 98% confidence interval for the true mean number of steps students take during the school day to be 8,500 to 10,200. If the teacher had used a 90% confidence interval rather than a 98% confidence interval, what would happen to the width of the interval?
Answer
A
It would increase by 8%.
B
It would decrease by 8%.
C
It would increase, but not necessarily by 8%.
D
It would decrease, but not necessarily by 8%.
Explanation
A lower confidence level uses a smaller critical value, so the margin of error—and therefore the interval’s width—would decrease. The change is not necessarily 8%: confidence level does not translate directly into the same percentage change in interval width. Thus, the width would decrease, but not necessarily by 8%.
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