U.S. textile company is interested in the proportion of orders shipped to another country. In a random sample of 1560 clothing orders placed to U.S. companies, 500 were exported.
a. Find a 99% confidence interval for the true proportion of clothing orders shipped to other countries.
b. In the previous year, the true proportion of clothing orders shipped to other countries was believed to be 0.30. Using your answer to part (a), is there any evidence to suggest the true proportion has changed? Justify your answer. Write a Solution Trail for this problem.
Many dairy farms have experienced bankruptcy over the past decade as a result of wild fluctuations in conventional milk prices. However, organic farms, those that do not treat cows with antibiotics or hormones and use hay grown without chemicals, have remained solvent and even expanded. In a random sample of 1400 New England dairy farms, 90 are certified as organic.
a. Find a 99% confidence interval for the true proportion of New England dairy farms certified as organic.
b. Five years ago, an extensive census reported that 3% of all New England dairy farms were organic. Is there any evidence to suggest this proportion has changed? Justify your answer.