c) A student is working on his science fair project. He hypothesizes that the average height of a certain native plant is normally distributed with = 10 cm, but he isn't sure what the variance is. To test his theory, he finds 25 mature plants and measures their heights. If he determines the average height of his sample to be 10.2 cm (S = 1.9), does he have evidence to support his hypothesis? i) How likely is the student to find an average height as tall as (or taller than) 10.2 cm, if his hypothesized population mean of 10 cm is correct? (That is, what is P(X> 10.2), under the assumption that μ = 10?) ii) Does the student have evidence to support his hypothesis? (That is, is he likely to find a sample like the one he found, assuming that μ = 10 in is true?) Circle YES or NO and briefly explain your answer. YES NO

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