Question

A survey was sent to 180 randomly selected juniors asking if they are interested in attending prom. Of the 180 interviewed, 49 said yes, 18 said no, and 113 had no opinion. A confidence interval was constructed from the data to estimate the proportion of juniors who were not interested in attending prom. Is the confidence interval valid? Explain.

Answer 1

Sample proportion of juniors who were not interested in attending prom p̂ = 18/180 = 0.10

For confidence interval to be valid, sampling distribution of distribution proportion should be approximately normal.

The condition that must be met for sampling distrbution of p̂ to be approximately normal are as follows:

np ≥ 10 & n*(1-p) ≥ 10

In this case, n = 180 and p = 0.10

np = 180*0.10 = 18 ≥ 10 (Condition satisfied)

n*(1-p) 180*(1-0.10) = 162 ≥ 10 (Condition satisfied)

Thus, it can be said that, confidence interval is valid