Biting an unpopped kernel of popcorn hurts! As an experiment, a self-confessed connoisseur of cheap popcorn carefully counted 773 kernels and put them in a popper. After popping, the unpopped kernels were counted. There were 86.

a) Construct a 90% confidence interval for the proportion of all kernels that would not pop.

b) Check the normality assumption.

c) Try the Very Quick Rule. Does it work well here? Why or why not?

d) Why might this sample not be typical?

NOTE: The Very Quick Rule (VQR) for a 95% confidence interval when p is near .50 is p+/-  1/square root n.

The VQR begins to fail when p is outside the range .40 < p < .60. For example it works poorly for the Ameritech example because p = .15. However, the VQR may be useful in making a quick assessment.