A farmer wants to grow bigger tomatoes, and injects a strain of tomatoes with a growth hormone to see if it makes them bigger than normal tomatoes. We assume the population of normal, untreated tomatoes has a weight of μ = 50 and σ = 20 considering the distribution of sample means from selecting several random samples of N = 15 tomatoes. The strain of treated tomatoes has a mean weight (M) of 100.

a. Calculate the standard error of the distribution of sample means for the population of normal, untreated tomatoes. Remember, this is the distribution of sample means corresponding to the original, untreated population.

b. What is the most likely weight for an untreated tomato?

c. Find the weight of a normal tomato (i.e. an untreated tomato) at z = – 1.96, and z = 1.96. Does it appear the farmer’s growth hormone treatment made his tomatoes bigger? Why or why not?

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