. To determine the effectiveness of a new safety control system in an industrial plant the number of accidents were measured for two weeks before and two weeks after its installation. The following data were obtained: 3 and 1 5 and 2 2 and 0 3 and 2 3 and 2 3 and 0 0 and 2 4 and 3 1 and 3 6 and 4 4 and 1 1 and 0 Use the paired sample sign test to test, at level 0.05, whether or not the new system is effective.
Using sample data, we compute the standard deviation of the differences (s), the standard error (SE) of the mean difference, the degrees of freedom (DF), and the t statistic test statistic (t).
where di is the observed difference for pair i, d is mean difference between sample pairs, D is the hypothesized mean difference between population pairs, and n is the number of pairs.
Since we have a two-tailed test, the P-value is the probability that a t statistic having 11 degrees of freedom is more extreme than 2.53; that is, less than - 2.53 or greater than 2.53.
P-value = P(t < - 2.53) + P(t > 2.53)
Use the excel formula , "=T.DIST.2T(2.53,11)" for finding p-values.
P-value = 0.0280
Interpret results. Since the P-value (0.0280) is less than the significance level (0.05), we have to reject the null hypothesis.
Reject H0. Hence the new system is effective.
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