Research at the University of Manitoba has resulted in the development of high yielding, high protein soybeans particularly suited to the local climate. There has been rapid growth in the land area planted with these soybeans, many of which are not genetically modified (non-GMO), making them suitable for export to the European Union. A survey of 420 soybean farmers found 85% of them grew non-GMO soybeans.

a) Calculate a 90% confidence interval for this proportion, stating your assumptions clearly. Interpret its meaning.

b) How much wider would this confidence interval have been if we had only surveyed 210 soybean farmers?

c) How many times wider would a 99% confidence interval be?

d) Five years later, a survey of 285 soybean farmers found that 80% of them grew non-GMO soybeans. Are we 95% confident that the proportion of farmers growing non- GMO soybeans is going down?