Statistics Three Problems Assignment

Assume, unless otherwise noted, that ?=0.05

1.Suppose a farmer has many plots of land (each 20m x 40m) on which she grows two different varieties of wheat. She plants variety A on 35% of her plots and variety B on the remaining 65%. She knows that the yield for variety A plots is approximately normally distributed, with a mean of 84 kg and a standard deviation of 11 kg. The yield for variety B plots is also normally distributed with a mean of 91 kg and a standard deviation of 17 kg.

a.What yield from a variety A plot corresponds to the 90th percentile for that variety?

b.Overall, what proportion of her plots yield less than 80 kg?

c.If you randomly select a plot that yieldedmorethan 80 kg, what is the probability that the plot had variety B planted on it?

2.In a clinical trial, researchers tested a new drug on a random sample of patients suffering from insomnia. The drug was designed to increase the number of hours of sleep patients get overnight.

a.If the p-value for the hypothesis test in the study is 0.03, what would be your conclusion in the context of the problem?(2pt)

3.In a population of lab mice, their weights at 30 days of age follow a normal distribution with a mean of 9.1 g and standard deviation of 1.2 g.

a.What is the probability that a random sample of n=35 mice would have a mean weight less than 8.6 g?

b.Suppose that you knew that the population distribution of mice weights was in fact positively skewed, but still had the same mean and standard deviation. Would you expect this to change your results in part (a)? Why/why not?