Discussion
Failing to reject a null hypothesis when it is false is termed as :
Answer: B
Failing to reject a false null hypothesis is a Type II error.
A Type II error (probability beta) occurs when the null hypothesis is actually false but the test fails to reject it, so a real effect or difference is missed. Its probability falls as sample size, effect size or the significance level rises; the power of a test is \(1 - \beta\).
A Type I error is the opposite: rejecting a null hypothesis that is true, with probability alpha. Sampling error is the chance difference between a sample statistic and the population value, and non-sampling errors arise from measurement, non-response or processing; neither is defined by a wrong decision about the null hypothesis.
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