Question

a graduate student wanted to estimate the average time spent studying among graduate students at her school. she randomly sampled graduate students from her school and obtained a 99% confidence interval of (17,25) hours/week. what is the margin of error?
choose the correct answer below.
a. 8 hours/week
b. 4 hours/week
c. 1.96
d. 1%
e. 21 hours/week

Explanation:

Step1: Recall the formula for confidence interval

The confidence interval is given by \(\bar{x}-E\) (lower bound) and \(\bar{x} + E\) (upper bound), where \(E\) is the margin of error. The formula for the margin of error \(E=\frac{\text{Upper bound}-\text{Lower bound}}{2}\)

Step2: Substitute the values of upper and lower bounds

Here, the lower bound \(L = 17\) and the upper bound \(U=25\). Then \(E=\frac{25 - 17}{2}\)

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Answer:

B. 4 hours/week