There has been rapid growth in the land area planted with high yielding, high protein soybeans particularly suited to local climate, many of which are not genetically modified (non-GMO). A survey of 392 soybean farmers found that 72% of them grew non-GMO soybeans. a. Calculate a 95% confidence interval for this proportion, stating your assumptions clearly. b. How much wider or narrower would this confidence interval have been if only 98 soybean farmers had been surveyed? c. How many times wider or narrower would a 90% confidence interval be?
There has been rapid growth in the land area planted with high yielding, high protein soybeans particularly suited to local climate, many of which are not genetically modified (non-GMO). A survey of 392 soybean farmers found that 72% of them grew non-GMO soybeans.
a. Calculate a 95% confidence interval for this proportion, stating your assumptions clearly.
b. How much wider or narrower would this confidence interval have been if only 98 soybean farmers had been surveyed?
c. How many times wider or narrower would a 90% confidence interval be?
d. Four years later a survey of 276 soybean farmers found that 68% of them grew non-GMO soybeans. Can it be said with 99% confidence that the proportion of farmers growing non-GMO soybeans has changed
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