Some Psychologists Hypothesize That a Family History of Speech Communication

Some psychologists hypothesize that a family history of speech communication
disorder might be a factor in speech delay. The theory is that if members of the
family have difficulty communicating, this may increase the probability of a speech
delay in a young family member. Random samples of healthy two-year-olds from
families with speech communication disorders and from families with no speech
communication disorder were followed over the course of a year. At age 3, each
child was classified as having a speech delay or not. These data are shown in the
table below: Speech delay and gender at 3 years old
$\begin{array}{|c|c|c|c|}\hline \begin{array}{c}\text { Family history of } \\\text { Speech communication } \\\text { disorder }\end{array} & \begin{array}{c}\text { Speech } \\\text { Delay }\end{array} & \begin{array}{c}\text { No } \\\text { Speech Delay }\end{array} & \text { Total } \\\hline \text { With } & 36 & 135 & 171 \\\text { Without } & 64 & 404 & 468 \\\text { Total } & 100 & 539 & 639 \\\hline\end{array}$
a) Construct a $95 \%$ confidence interval for the difference between the population proportions of healthy two-year-olds from families with speech communication disorders who have a speech delay and this proportion for those from families without speech communication disorders. b) Referring to your work in part (a), does there appear to be a difference between
the population proportions of healthy two-year-olds from families with speech
communication disorders who have a speech delay and this proportion for those
from families without speech communication disorders? Provide statistical
justification for your answer.
c) Is this an observational study or an experiment? Justify your response in a few
sentences.