Chapter 5.3, Problem 5.27ACB

Tomato as a taste modifier. Miraculin is a protein naturally produced in a rare tropical fruit that can convert a sour taste into a sweet taste. Refer to the Plant Science (May 201 0) investigation of the ability of a hybrid tomato plant to produce miraculin, Exercise 4.99 (p. 239). Recall that the amount x of miraculin produced in the plant had a mean of 105.3 micrograms per gram of fresh weight with a standard deviation of 8.0. Consider a random sample of n = 64 hybrid tomato plants and let $\bar{x}$ represent the sample mean amount of miraculin produced. Would you expect to observe a value of $\bar{x}$ less than 103 micrograms per gram of fresh weight? Explain.