Rice is a staple food for much of the world’s population. The height of a rice plant (usually 0.4–5 mm) depends on the rice variety and the environment. Genetic engineering is currently underway to...

Rice is a staple food for much of the world’s population. The height of a rice plant (usually 0.4–5 mm) depends on the rice variety and the environment. Genetic engineering is currently underway to protect rice plants from disease and to decrease the variability in plant height. In a controlled experiment, plant heights were measured (in millimeters); 30 natural rice plants had a sample variance in height of 1.5 mm, and 22 genetically engineered rice plants had a sample variance in height of 0.89 mm. Assume normality.

 a. Find a 95% confidence interval for the true variance in height for natural rice plants.

 b. Find a 95% confidence interval for the true variance in height for genetically engineered rice plants.

c. Is there any evidence to suggest the population variance is different for natural and genetically engineered rice plants?

In June 2013 the Agriculture Department banned all high-calorie sports drinks and candy bars from school vending machines.44 Many beverage companies had already added sports drinks to replace high-calorie sodas. The new rules stipulate that sports drinks must contain 60 calories or less in a 12-ounce serving. A random sample of sports drinks was obtained, and the calories in each was recorded.

 a. Find a 95% confidence interval for the population variance in calories for sports drinks.

b. Find a 95% confidence interval for the population standard deviation in calories for sport drinks.