Suppose that the study were repeated in a different inner city neighborhood and that out of 50 randomly sampled 18 -year-old women, 6 reported that they were taking birth control pills. The researchers would like to assess the evidence that the proportion of 18 -year-old women using birth control pills in this neighborhood is greater than the national average of \(5 \%\).

(a) Can the normal approximation to the binomial distribution be used to conduct a hypothesis test of the null hypothesis that the proportion of women using birth control pills in this neighborhood is equal to 0.05 ? Explain your answer.

(b) State the hypotheses for the analysis of interest and compute the \(p\)-value.

(c) Interpret the results from part (b) in the context of the data.