Question

In a test of Murphy’s law, pieces of toast were buttered on one side and then dropped. Mur- phy’s law predicts that they will land butter-side down. Out of 9821 slices of toast dropped, 6101 landed butter-side down. (Believe it or not, these are real data!10) a. What is a 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 land- ing butter-side down or butter-side up?

Answer 1

a) =(0.6116259, 0.6308137)

(b) No, because the interval does not include 0.5

Explanation:

Given Data:

sample size, n = 9821

Sample, x = 6101

(a) sample proportion
`p = (6101)/(9821) = 0.6212198`

Given a=0.05,

so Z(0.025) = 1.96 [via. standard normal table)

So 95% confidence interval is

`p \pm Z* \sqrt{(p* ((1-p))/(n))}`

`=  0.6212198 \pm 1.96* \sqrt{(0.6212198* ((1-0.6212198))/(9821))`

=(0.6116259, 0.6308137)

(b) No, because the interval does not include 0.5