Trends in fashion have signaled the emergence of green as the color of the century. It ranked third as the most preferred color among designers having a market share of 9.24%. Its popularity may be partially due to an increased interest in the environment. Besides, “Green symbolizes harmony and counteracts emotional stress.”
a. To verify the accuracy of these figures, a survey is being considered. Find the size of the sample that you should take if you want the estimate of the true proportion of designers who preferred green not to differ by more than 0.03 with 95% confidence.
b. Due to financial constraints, only a random sample of 250 local designers were interviewed and asked about their preferred color. Results showed that 27 preferred the color green. Construct a 95% confidence interval for the true proportion of local designers who preferred the color green. Interpret your results.
c. From the results in (b), is there sufficient evidence to indicate that the proportion of local designers who preferred the color green is different from 9.24%? Justify your answer.
3 answers