Sam works as a forest ranger and spends many nights in the wilderness, often relying on battery-operated lamps for light. He wants to know whether one of the top 2 brands of batteries would last longer in his lamps, giving him more hours of light before needing replacement. To see whether there is any difference between the two brands, he chooses 7 battery-powered lamps (each lamp requires 1 battery each) to test the batteries in. For each lamp, he then randomly chooses one of the brands, puts a fresh battery of that brand in the lamp, turns the lamp on, and records how long the battery lasts. He then repeats the experiment with a battery of the brand not used in the first trial for each toy. a. What kind of t-test would be appropriate to use? List two assumptions that are necessary to conduct this test properly. b. Write the null and alternative hypotheses. Is it a one-directional or nondirectional (bidirectional) hypothesis? c. In order to reject the null hypothesis with an alpha level of 0.05, what is the t-value one needs to obtain?
Sam works as a forest ranger and spends many nights in the wilderness, often relying on battery-operated
lamps for light. He wants to know whether one of the top 2 brands of batteries would last longer in his
lamps, giving him more hours of light before needing replacement. To see whether there is any difference
between the two brands, he chooses 7 battery-powered lamps (each lamp requires 1 battery each) to test
the batteries in. For each lamp, he then randomly chooses one of the brands, puts a fresh battery of that
brand in the lamp, turns the lamp on, and records how long the battery lasts. He then repeats the
experiment with a battery of the brand not used in the first trial for each toy.
a. What kind of t-test would be appropriate to use? List two assumptions that are necessary to
conduct this test properly.
b. Write the null and alternative hypotheses. Is it a one-directional or nondirectional (bidirectional)
hypothesis?
c. In order to reject the null hypothesis with an alpha level of 0.05, what is the t-value one needs
to obtain?
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