A New Brand of Chocolate Bar Is Being Market Tested $$\begin{array} { l c } \text { Response } & \text { Frequency } \\\text { Liked } & 300 \\\text { Disliked } &{ 100 }\\& { 400 }\end{array}$$

Short Answer

A new brand of chocolate bar is being market tested. Four hundred of the new chocolate bars were given to consumers to try. The consumers were asked whether they liked or disliked the chocolate bar. You are given their responses below.
$$\begin{array} { l c } \text { Response } & \text { Frequency } \\\text { Liked } & 300 \\\text { Disliked } &{ 100 }\\& { 400 }\end{array}$$
a. What is the point estimate for the proportion of people who liked the chocolate bar?
b. Construct a 95% confidence interval for the true proportion of people who liked the chocolate bar.
c. With a .95 probability, how large of a sample needs to be taken to provide a margin of error of 3% or less?