Suppose that a study compared firms with and without sophisticated postaudit procedures. A random sample of 31 matched pairs of firms was examined. For each firm the ratio of market valuation to replacement cost of assets was computed as a measure of firm performance. In each of the 31 pairs, one firm employed sophisticated postaudit procedures and the other did not. The 31 differences in ratios were calculated, and the absolute differences were ranked. The smaller of the rank sums, 189, was for those pairs where the ratio was higher for the firm without sophisticated postaudit procedures. Test the null hypothesis that the distribution of differences in ratios is centered on 0 against the alternative that the ratio of market valuation to replacement cost of as- sets tends to be lower for firms without sophisticated postaudit procedures
Suppose that a study compared firms with and without sophisticated postaudit procedures. A random sample of 31 matched pairs of firms was examined. For each firm the ratio of market valuation to replacement cost of assets was computed as a measure of firm performance. In each of the 31 pairs, one firm employed sophisticated postaudit procedures and the other did not. The 31 differences in ratios were calculated, and the absolute differences were ranked. The smaller of the rank sums, 189, was for those pairs where the ratio was higher for the firm without sophisticated postaudit procedures. Test the null hypothesis that the distribution of differences in ratios is centered on 0 against the alternative that the ratio of market valuation to replacement cost of as- sets tends to be lower for firms without sophisticated postaudit procedures
Solution :
Given : n = 31 and Test statistic (T) = 189
Let,
H0 : Distribution of the differences in ratio of market valuation to replacement cost of assets centered on 0.
H1 : Distribution of the differences in ratio of market valuation to replacement cost of assets tends to be lower.
To test this Hypothesis Wilcoxon Signed Rank Test is used.
If n is large ( > 20) then random variable has standard normal distribution.
i.e. z =
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