A. Computer software generated 500 random numbers that should looklike they are

Question

A.
Computer software generated 500 random numbers that should looklike they are from the standard Normal distribution. The arecategorized into 5 groups:(1)less than or equal to -0.6
(2)greater than -.6 and less than or equal to -.1 (3) greater than-.1 and less than or equal to .1 (4)greater than .1 and less thanor equal to .6 and (5)greater than .6. The counts in the fivegroups are 139,102,41,78, and 140 respectively. Find theprobabilities for these five intervals using Table A. Then computethe expected number for each interval for a sample of 500. Finally, perform the goodness of fit test and summarize yourresults.

Explanation / Answer

Null Hypothesis: There is no significancedifference between the observed values and the expectedvalues Alternative Hypothesis: There is a significancedifference between the observed values and the expectedvalues Consider the following table Groups Counts(Oi) p(x) E=N*p(x) (Oi-Ei)^2 (Oi-Ei)^2/Ei 1 139 0.2 100 1521 15.21 2 102 0.2 100 4 0.04 3 41 0.2 100 3481 34.81 4 78 0.2 100 484 4.84 5 140 0.2 100 1600 16 Total(N) 500 70.9 Groups Counts(Oi) p(x) E=N*p(x) (Oi-Ei)^2 (Oi-Ei)^2/Ei 1 139 0.2 100 1521 15.21 2 102 0.2 100 4 0.04 3 41 0.2 100 3481 34.81 4 78 0.2 100 484 4.84 5 140 0.2 100 1600 16 Total(N) 500 70.9
THe degrees of freeedom = 5-1 =4df and thecritical value of of the chi-square at 0.05, the level ofsignificance is 9.49 Since the calculated value of chi-squaers isgreater than the critical value of chi-squaer so we conclude thatthere is a significance difference between the observed values andthe expected values Groups Counts(Oi) p(x) E=N*p(x) (Oi-Ei)^2 (Oi-Ei)^2/Ei 1 139 0.2 100 1521 15.21 2 102 0.2 100 4 0.04 3 41 0.2 100 3481 34.81 4 78 0.2 100 484 4.84 5 140 0.2 100 1600 16 Total(N) 500 70.9

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