HW 3 ezto.mheducation.com/hm.tpx A software company develops and markets a popul

Question

HW 3 ezto.mheducation.com/hm.tpx A software company develops and markets a popular business simulation/modeling program. A random number generator contained in the program provides random values from various probability distributions The software design group would like to validate that the program is properly generating random numbers Accordingly, they generated 5,000 random numbers from a normal distribution and grouped the results into the frequency distribution shown below The sample mean and sample standard deviation are 100 and 10 respectively Use Table 3 Under 70 70 up to 80 80 up to 90 90 up to 100 100 up to 110 110 up to 120 120 up to 130 130 or more 12 658 1734 1681 697 112 Total 5,000 a. Using the goodness-of-fit test for normality, state the competin hypotheses to test if the random Hy Random numbers are normally distributed with a mean of 100 and a standard deviation of 10. O Ho Random numbers are not normally distributed with a mean of 100 and a standard deviation of numbes generated do not follow the normal distribution HA Random numbers are not normally distributed with a mean of 100 and a standard deviation of 10 10. HA Random numbers are normally distributed with a mean of 100 and a standard deviation of 10. b. What is the critical value at the 1% significance level? (Round your answer to 3 decimal places.) Critical value c Calculate the value of the test statistic (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) Test statistic d-1. What is the conclusion to the test? Click to select) ,1% Alte 1%serificance lever wel(Click to select) that generated are not normally distributed d-2. Is your conclusion sensitive within the range of typical signficance levels (10% or below)? Yes O No Type here to search

Explanation / Answer

a)

Ho: random numebrs are normally distributed...............

Ha:  random numebrs are not normally distributed...........

b)

for degree of freedom =categories -1 =8-1 =7

for 7 degree of freedom ; critical value =18.475

c)

test statistic =6.880

d-1)

fail to reject Ho; at the 1%........we do not have suffciient evidence to conclude that.............

d-2)

Yes

Class Limits observed Normal Normal Expected 2=(O-E)2/E lower Upper Bin frequency(O) probabilty probabilty(p) frequency(E=p*O) - 70 -70 12 P(X<70) 0.0013 6.749 4.084 70 - 80 70-80 99 P(70<X<80) 0.0214 107.001 0.598 80 - 90 80-90 658 P(80<X<90) 0.1359 679.526 0.682 90 - 100 90-100 1734 P(90<X<100) 0.3413 1706.724 0.436 100 - 110 100-110 1681 P(100<X<110) 0.3413 1706.724 0.388 110 - 120 110-120 697 P(110<X<120) 0.1359 679.526 0.449 120 - 130 120-130 112 P(120<X<130) 0.0214 107.001 0.234 130 - 130- 7 P(130<X<) 0.0013 6.749 0.009 Total 5000 1 5000 6.880

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