In hypothesis testing, why are verbal problem statements converted to numerical problem statements?
It’s just good practice in any mathematical problem to translate the words into mathematical symbols. It’s the same as translating one language into another. Consider the hypothesis as a trial against the null hypothesis. The data is evidence against the mean. You assume the mean is true and try to prove that it is not true. After finding the test statistic and p-value, if the p-value is less than or equal to the significance level of the test we reject the null and conclude the alternate hypothesis is true. If the p-value is greater than the significance level then we fail to reject the null hypothesis and conclude it is plausible. Note that we cannot conclude the null hypothesis is true, just that it is plausible. If the question statement asks you to determine if there is a difference between the statistic and a value, then you have a two tail test, the null hypothesis, for example, would be μ = d vs the alternate hypothesis μ ≠ d if the question ask to test for an inequality you ma
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