Answer to Question #258398 in Statistics and Probability for princess

Question

2. It is known that, when given a choice between ordering an espresso or a cappuccino, 63% of people will order the cappuccino. For a sample of 253 people, what is the probability that sampling error for the proportion will be greater than 0.05?

Answer 1

sampling error:

$z\sqrt{\frac{p(1-p)}{n}}>0.05$

$z\sqrt{\frac{0.63(1-0.63)}{253}}=0.03z>0.05$

$z>5/3=1.67$

the probability that sampling error for the proportion will be greater than 0.05:

$P(z>1.67)=1-P(z<1.67)=1-0.9525=0.0475$