Questions: Randomly sampled math majors at a large university were asked to take part in a survey about the curriculum. The dean wanted to find out how challenging the math coursework was for students. The proportion of math majors that stated the curriculum was challenging was 0.92 , with a margin of error of 0.07 . Construct a confidence interval for the proportion of math majors that stated the curriculum was challenging.

Randomly sampled math majors at a large university were asked to take part in a survey about the curriculum. The dean wanted to find out how challenging the math coursework was for students. The proportion of math majors that stated the curriculum was challenging was 0.92 , with a margin of error of 0.07 .

Construct a confidence interval for the proportion of math majors that stated the curriculum was challenging.

Transcript text: Randomly sampled math majors at a large university were asked to take part in a survey about the curriculum. The dean wanted to find out how challenging the math coursework was for students. The proportion of math majors that stated the curriculum was challenging was 0.92 , with a margin of error of 0.07 . Construct a confidence interval for the proportion of math majors that stated the curriculum was challenging.

Solution

Solution Steps

Step 1: Given Information

We are provided with the following information regarding the survey of math majors:

The proportion of math majors that stated the curriculum was challenging is \( p = 0.92 \).
The margin of error is \( E = 0.07 \).

Step 2: Calculate the Confidence Interval

To construct the confidence interval for the proportion of math majors who found the curriculum challenging, we use the formula for the confidence interval:

\[ \text{Confidence Interval} = (p - E, p + E) \]

Substituting the values:

\[ \text{Lower Bound} = 0.92 - 0.07 = 0.85 \] \[ \text{Upper Bound} = 0.92 + 0.07 = 0.99 \]

Thus, the confidence interval is:

\[ (0.85, 0.99) \]