Question

In a recent survey, 456 out of 600 people surveyed think that the subject of calculus is difficult.

1. What is the margin of error for a 90% confidence interval for the percent of people that find calculus difficult?

2. Calculate the 90% confidence interval to determine whether the sample data supports the conclusion that a majority of people think calculus is difficult.

Answer 1

1)  

Sample proportion = 456 / 600 = 0.76

Margin of error = Z/2 * Sqrt [ ( 1 - ) / n ]

= 1.645 * sqrt [ 0.76 * ( 1 - 0.76) / 600 ]

= 0.029

2)

90% confidence interval for p is

- Z/2 * Sqrt [ ( 1 - ) / n ] < p < + Z/2 * Sqrt [ ( 1 - ) / n ]

That is

- margin of error < p < + Margin of error

0.76 - 0.029 < p < 0.76 + 0.029

0.731 < p < 0.789

90% CI is ( 0.731 , 0.789 )

From confidence interval,

Since 0.50 does not contained in confidence interval ( and all values in CI are greater than 0.50),

We conclude that majority of the people thinks calculus is difficult.