Question

Consider a confidence interval for a proportion, in which p̂ = 0.44 and the SE=0.025.

a) Compute the 95% confidence interval.

b) Sketch the bootstrap distribution, assuming that it is bell-shaped. Put the correct numbers on the p̂ axis, and indicate the 2-std-dev range.

c) Explain your confidence interval, beginning the sentence with, “We are 95% confident that…”

Answer 1

b.)

We use STATKEY for the construction of bootstrap distribution. To do this , we select Bootstrap C.I for single proportion and then select 'edit data' and enter the 'count' as 44 and 'sample size' as 100. Then we generate 1000 samples for this data. In order to indicate the 2 std deviation range , we select 'Two-Tail' and set the confidence interval to 0.95. The Bootstrap Distribution looks like this:

c.)

We are 95% confident that the population parameter( p-hat) is between 0.391 and 0.489.

STATKEY reference for part(a):