Question

As part of a class project, Sarah and Geoffrey conducted a survey asking their peers whether they planned on taking a music class the next year.Of the 90 students they surveyed, 43 responded favorably. Sarah and Geoffrey calculated the margin of error for different confidence intervals.Their work is shown.Which student incorrectly found the margin of error and why?

Answer 1

We have to find the mistake in the calculations of the margin of error.

The survey and the margin of error have the following characteristics:

• The number of students surveyed is 90, so the sample size is n = 90.

,

• The sample proportion is p = 43/90 or approximately 0.48.

,

• For a 95% confidence interval, the critical value is z = 1.96 and for a 90% confidence interval, the value is z = 1.65.

The margin of error can be calculated with the following formula:

`ME=z_c\cdot\sqrt{(p(1-p))/(n)}`

Then, if we check each formula for Sarah and Geoffrey we can see that Geoffrey uses 133 in the denominator, a value that does not correspond to the sample size n, which is 90.

Answer: Geoffrey incorrectly found the margin of error because he used the wrong sample size [Option D]