1. A pain medication claims to provide at least 6.5 hours of relief. A sample of
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Question
1. A pain medication claims to provide at least 6.5 hours of relief. A sample of 12 headache sufferers took the medication and reported the following (ordered) durations of relief 3.5 3.8, 4.4, 4.9, 4.9, 5.1, 5.5, 6.3, 7.5, 8.1, 9.5, 9.8
(a) Use the sign test to look for evidence that the medication provides less relief than claimed. In doing so, specify the hypotheses and test statistic.
(b) Compute the p-value of this test, and make a decision at the 0.05 level. You may use the normal approximation (with or without continuity correction).
Explanation / Answer
a) Hypothesis
Ho: Median is less or equal to 6.5
H1: Median is greater than 6.5.
Sign Test for Median: Headache
Sign test of median = 6.500 versus > 6.500
N Below Equal Above P Median
Headache 12 8 0 4 0.9270 5.300
Conclusion: The estimated p-value is 0.93 and less than 0.05. Hence, we can reject the null hypothesis and also reject the medication claims to provide at least 6.5 hours of relief.
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