A study was undertaken to compare moist and dry storage conditions for their effect on the moisture content(%) of white pine timber. The report on the findings from the study included the following statement:"The study showed a significant difference (observed difference = 1.1%; p-value=0.023) in the moisture content of the pine timber under different storage conditions. Level of Significance (α) for the test was 5%."Based on this information, which of one the following statements is necessarily FALSE?Group of answer choicesThe probability that there is no difference between moist and dry storage conditions is 0.023The observed difference between the mean moisture contents (1.1%) is unlikely to be due to chance alone.If this study was repeated 100 times over, then we would expect to (incorrectly) conclude there was a difference in the storage methods for approximately 5 of the 100 studies (that is, 5% of the time we would say there was a difference in the storage methods when, in fact, there was none).A statistically significant difference of 1.1% in the moisture content of the white pine is not necessarily a difference of practical importanceIf the researchers used a large enough sample size then even a tiny difference could result in a statistically significant difference
Question
A study was undertaken to compare moist and dry storage conditions for their effect on the moisture content(%) of white pine timber. The report on the findings from the study included the following statement:"The study showed a significant difference (observed difference = 1.1%; p-value=0.023) in the moisture content of the pine timber under different storage conditions. Level of Significance (α) for the test was 5%."Based on this information, which of one the following statements is necessarily FALSE?Group of answer choicesThe probability that there is no difference between moist and dry storage conditions is 0.023The observed difference between the mean moisture contents (1.1%) is unlikely to be due to chance alone.If this study was repeated 100 times over, then we would expect to (incorrectly) conclude there was a difference in the storage methods for approximately 5 of the 100 studies (that is, 5% of the time we would say there was a difference in the storage methods when, in fact, there was none).A statistically significant difference of 1.1% in the moisture content of the white pine is not necessarily a difference of practical importanceIf the researchers used a large enough sample size then even a tiny difference could result in a statistically significant difference
Solution
The statement that is necessarily FALSE is: "The probability that there is no difference between moist and dry storage conditions is 0.023". The p-value of 0.023 does not represent the probability that there is no difference between the two storage conditions. Instead, it represents the probability of obtaining the observed difference (or a more extreme difference) if there was actually no difference between the two storage conditions (i.e., under the null hypothesis).
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