QUESTION 07 (10 points) ‐ Goodness‐of‐fit Test of the Normal Distribution (Test of Normality) Given a sample of 1739 data points, you need to test if the data come from a normal population at α = 0.05. The original data are transformed into z‐scores with the observed frequencies: Category x P(x) Observed Frequency (no observations for x = 7 or above) TOTAL 1.00000 584 αv 0.96 0.93 0.93 0.93 0.90 χ2 12.36467 11.12820 13.60113 14.83760 12.36467 df 5 7 6 5 6 Category z‐interval Expected Prob. Expected Freq. Observed Freq. (O ‐ E)2/E 1 2 3 4 5 6 7 (‐[infinity],‐2.5] (‐2.5 , ‐1.5] (‐1.5 , ‐0.5] (‐0.5 , 0.5] (0.5 , 1.5] (1.5 , 2.5] (2.5 , [infinity]] ? ? 0.06060 ? ? ? ? ? 0.24173 ? ? ? 0.00621 ? 15 ? 121 ? 392 675 ? 407 ? 116 ? 13 ? 1.91452 TOTAL 1.00000 ? 1739 ? (a)[0] Give an equation that shows how the original data are transformed into z‐scores. (b)[0] Form the null and alternative hypotheses H0 and H1. Make a sketch of the test. (c)[0] Specify appropriate equations for the χ2 statistic and degrees of freedom df. (d)[1] Calculate the remaining probabilities with Excel lookups in Hint.