One of the Most Striking Human Accomplishments Is the Achievement

Essay

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.