Question

From a survey of 278 McMaster students, you find that 68% take the bus to McMaster everyday. Find the margin of error for a 99% confidence level (assume z 0.005 =2.58 ). Note: 1- Only round your final answer to

3 decimal places. Enter your final answer with 3 decimal places.

Answer 1

The margin of error is calculated using the formula for a sample proportion and comes out to be 0.072 when rounded to three decimal places.

Step-by-step explanation:

The student's question pertains to finding the margin of error with a given confidence level and sample proportion. Using the given data, we can calculate the margin of error following the formula:

Margin of Error (E) = z * sqrt((p*(1-p))/n)

Where:

z is the z-value corresponding to the confidence level (2.58 for 99%).

p is the sample proportion (0.68).

n is the sample size (278).

Plugging the numbers into the formula:

E = 2.58 * sqrt((0.68 * (1 - 0.68)) / 278)

Calculating the margin of error:

E = 2.58 * sqrt((0.68 * 0.32) / 278)

E = 2.58 * sqrt(0.2176 / 278)

E = 2.58 * sqrt(0.000782733)

E = 2.58 * 0.0279798619

E = 0.0722095435

Therefore, after rounding to three decimal places, the margin of error is 0.072.