7. Suppose that a certain species of tomato plant has been extensively studied. It has been found that the distribution of the diameters of these tomatoes is roughly bell-shaped with light-tails. In order to test whether a new growth hormone produces larger tomatoes, a botanist decides to conduct a hypothesis test. If µ denotes the true mean of tomatoes with the growth hormone and 42 denotes untreated tomatoes, then her hypotheses are Ho : i = 2 vs. HA : H1 > µ2. She randomly samples 6 tomatoes, applies the new growth hormone to 3 of them, and measures the following diameters (in cm).

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7.
has been found that the distribution of the diameters of these tomatoes is roughly bell-shaped
with light-tails. In order to test whether a new growth hormone produces larger tomatoes, a
botanist decides to conduct a hypothesis test. If u denotes the true mean of tomatoes with
the growth hormone and u2 denotes untreated tomatoes, then her hypotheses are Ho : 41 = µ2
vs. HA : µ1 > 42. She randomly samples 6 tomatoes, applies the new growth hormone to 3 of
them, and measures the following diameters (in cm).
Suppose that a certain species of tomato plant has been extensively studied. It
Experimental Group 12.7 13.4 13.9
Control Group
9.7
10.4
13.1
(a) Explain why the two-sample t-test is the appropriate hypothesis test for the botanist to
perform.
(b) Based on the two sample t-test, is there sufficient evidence to reject Ho in favour of HA at
the a = 0.15 significance level?
Transcribed Image Text:7. has been found that the distribution of the diameters of these tomatoes is roughly bell-shaped with light-tails. In order to test whether a new growth hormone produces larger tomatoes, a botanist decides to conduct a hypothesis test. If u denotes the true mean of tomatoes with the growth hormone and u2 denotes untreated tomatoes, then her hypotheses are Ho : 41 = µ2 vs. HA : µ1 > 42. She randomly samples 6 tomatoes, applies the new growth hormone to 3 of them, and measures the following diameters (in cm). Suppose that a certain species of tomato plant has been extensively studied. It Experimental Group 12.7 13.4 13.9 Control Group 9.7 10.4 13.1 (a) Explain why the two-sample t-test is the appropriate hypothesis test for the botanist to perform. (b) Based on the two sample t-test, is there sufficient evidence to reject Ho in favour of HA at the a = 0.15 significance level?
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