quiz9_key(1)

# quiz9_key(1) - NAME Stat 205 Quiz 9 1(3 points Suppose a 95...

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Unformatted text preview: NAME: Stat 205 Quiz 9 1. (3 points) Suppose a 95% conﬁdence interval for µ1 − µ2 is (−3.1, −1.7). If we test H0 : µ1 − µ2 = 0 versus HA : µ1 − µ2 = 0 using α = 0.05, will we reject H0 ? Why or why not? (2 points) What can you say about the p-value for testing H0 ? Answer: Since the hypothesized difference of zero is not in the 95% conﬁdence interval, we reject H0 at the 5% level. Because we reject, we know that the p-value is less than 0.05. 2. (7 points) An entomologist conducted an experiment to see if wounding a tomato plant would induce changes that improve its defense against insect attack. She grew larvae of the tobacco hornworm on both wounded and control plants. The table below has summary statistics from the two groups of larval weights (mg) after a week of growth. Let HA be that wounding the plant diminishes larval growth. How strongly do the data support the researcher’s expectation? Construct the appropriate statistic ts and report a p-value (perhaps by bounding), from a t-test. Carry out the test at the α = 0.05 level. Formula (7.1) gives 31.8 df. Larval growth on wounded plants n 16 y ¯ 28.66 s 9.02 Larval growth on control plants 18 37.96 11.14 Answer: 9.022 11.142 + = 3.46. 16 18 28.66 − 37.96 ts = = −2.69. 3.46 The alternative is HA : µ1 < µ2 where µ1 is the mean wounded plant larval growth and µ2 is the mean control plant larval growth. Bounding the p-value using the t critical table (with df=30) we get 0.005 < p < 0.01. We reject at the 5% level because p < 0.01 < 0.05 = α. SEy1 −y2 = ¯¯ ...
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