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Testing whether a firm underpays its traders

Question

Across the industry, trader pay has mean 132132 and standard deviation 2525. A prop firm's 4040 traders are paid an average of 122122. At significance level 0.010.01 (critical value z=−2.326z=-2.326), is there evidence that the firm pays below the industry norm? Answer 11 for yes and 00 for no.

Short answer

11 (yes). The one-sided statistic is z=122−13225/40≈−2.53z=\dfrac{122-132}{25/\sqrt{40}}\approx-2.53, which lies below −2.326-2.326, so the null of industry-standard pay is rejected.

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