Math  /  Data & Statistics

QuestionQuestion 1 1 pts
A standard painkiller is known to bring relief in 3.5 minutes on average ( μ\mu ). A new painkiller is hypothesized to bring faster relief to patients.
A sample of 40 patients are given the new painkillers. The sample yields a mean of 2.8 minutes and a standard deviation of 1.1 minutes.
Which of the following pairs of hypotheses are appropriate for this study? H0:μ=2.8H_{0}: \mu=2.8 vs. Ha:μ2.8H_{a}: \mu \neq 2.8 H0:μ=2.8H_{0}: \mu=2.8 vs. Ha:μ<2.8H_{a}: \mu<2.8 H0:μ=3.5H_{0}: \mu=3.5 vs. Ha:μ<3.5H_{a}: \mu<3.5 H0:μ=3.5H_{0}: \mu=3.5 vs. Ha:μ=2.8H_{a}: \mu=2.8 H0:μ=3.5H_{0}: \mu=3.5 vs. Ha:μ>3.5H_{a}: \mu>3.5

Studdy Solution
The new painkiller is hypothesized to bring faster relief, meaning the average relief time should be less than 3.5 minutes. Therefore, the alternative hypothesis Ha H_a should reflect this claim:
Ha:μ<3.5 H_a: \mu < 3.5
The appropriate pair of hypotheses for this study is:
H0:μ=3.5vs.Ha:μ<3.5 H_0: \mu = 3.5 \quad \text{vs.} \quad H_a: \mu < 3.5

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