Question

22. In a test of Murphy's Law, pieces of toast were buttered on one side and then dropped. Murphy's Law predicts that they will land butter-side down. Out of 9821 slices of toast dropped, 6101 landed butter-side down.

(a). What is the 95% confidence interval for the probability of a piece of toast landing butter-side down?

(b). Using the results of part (a), is it plausible that there is a 50:50 chance of the toast landing butter-side down or butter-side up?

Answer 1

a)

Sample proportion = 6101 / 9821 = 0.621

95% confidence interval for p is

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

0.621 - 1.96 * sqrt [ 0.621 * ( 1 - 0.621) / 9821] < p < 0.621 + 1.96 * sqrt [ 0.621 * ( 1 - 0.621) / 9821]

0.611 < p < 0.631

95% CI is ( 0.611 , 0.631 )

b)

Since 0.50 is not contained in the confidence interval, it is not plausible that there is 50:50 chance

of the toast landing butter-side down or butter-side up