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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?

Respuesta :

Answer:

a) =(0.6116259, 0.6308137)

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

Step-by-step explanation:

Given Data:

sample size, n = 9821

Sample, x = 6101

(a) sample proportion [tex]p = \frac{6101}{9821} = 0.6212198[/tex]

Given a=0.05,

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

So 95% confidence interval is

[tex]p \pm Z\times \sqrt{(p\times \frac{(1-p)}{n})}[/tex]

[tex]=  0.6212198 \pm 1.96\times \sqrt{(0.6212198\times \frac{(1-0.6212198)}{9821})[/tex]

=(0.6116259, 0.6308137)

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

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