One of the Most Striking Human Accomplishments Is the Achievement

One of the most striking human accomplishments is the achievement of intelligible
speech by age five. Males generally develop at a slower rate than females, and in a
recent large study of speech development in young children, investigators
hypothesized that a greater proportion of boys would have speech deficits for this
reason. Random samples of healthy two-year-old males and females were followed
over the course of a year, and at age 3 each child was classified as having a speech
deficit or not. The data are given in the table below: $$\begin{array}{l}\text { Speech delay and gender at } 3 \text { years old }\\\begin{array} { | l | c | c | c | } \hline { \text { Gender } } & \begin{array} { c } \text { Speech } \\\text { deficit }\end{array} & \begin{array} { c } \text { No Speech } \\\text { Deficit }\end{array} & \text { Total } \\\hline \text { Female } & 22 & 280 & 302 \\\text { Male } & 78 & 259 & 337 \\\text { Total } & 100 & 539 & 639 \\\hline\end{array}\end{array}$$ a) Construct a 95% confidence interval for the difference between the population
proportions of males and the proportion of females at this school who would be
classified as having a speech deficit.
b) Referring to your work in part (a), does there appear to be a difference between
the population proportions of males and females at this school who would be
classified as having a speech deficit? Provide statistical justification for your
answer.
c) Is this an observational study or an experiment? Justify your response in a few
sentences.