Question

(a). A simple random sample of 37 days was selected. For these 37 days, Parsnip was fed seeds on 22 days and Parsnip was fed pellets on the other 15 days. The goal is to calculate a 99% confidence interval for the proportion of all days in which Parsnip was fed seeds, and to do so there are two assumptions. The first is that there is a simple random sample, which is satisfied. What is the second assumption, and specific to the information in this problem, is it satisfied? Explain why or why not.

(b). If appropriate, use the data in part (a) to calculate and interpret a 99% confidence interval for the proportion of all days in his life that Parsnip has been fed seeds.

Answer 1

a) the following interval calculations for the proportion confidence interval is dependent on the following assumptions being satisfied: np ≥ 10 and n(1-p) ≥ 10. If p is unknown then use the sample proportion

So, n=37

sample proportion ==22/37 and

(1-​​​​​​) =(1-22/37)=15/37

Now,n*>10

n*(1-​​​​​​) >10

The conditions are met.

b)