Question

Using the K-S Test, determine if it is reasonable to assume that the data given in column A came from a uniform distributionbetween 0 and 100. Show your results below using a Type I error of 5%: (Note, for the p-value estimate, if it is greater than 10%, write “>10%”; if it is less than 1%, write “<1%”; otherwise, use linear interpolation. Value for the Dn = max {D+ , D- } statistic: Value for the KS test statistic: Critical value for the KS statistic:    Estimate of p-value: Delete the line that does not apply: Conclusion: Fail to reject H0, the data may have come from an uniform distribution Conclusion: Reject H0, the data may not have come from an uniform distribution

Data

88.3

91.7

98.8

32.4

20.6

76.6

40.7

67.3

90.1

87.8

73.1

73.2

36.3

7

17.2

69.8

21.6

27.3

27.3

45.2

23.7

62.6

6

87.6

36.8

23.3

97.4

99.7

45.3

87.2

Answer 1

R code:

Data=c(88.3,91.7,98.8,32.4,20.6,76.6,40.7,67.3,90.1,87.8,73.1,73.2,36.3,7.0,17.2,
69.8,21.6,27.3,27.3,45.2,23.7,62.6,6.0,87.6,36.8,23.3,97.4,99.7,45.3,87.2)
ks.test(Data,"punif",0,100)

Output:

One-sample Kolmogorov-Smirnov test

data: Data
D = 0.172, p-value = 0.3373
alternative hypothesis: two-sided

Warning message:
In ks.test(Data, "punif", 0, 100) :
ties should not be present for the Kolmogorov-Smirnov test

Value for the KS test statistic=0.172

Critical value=0.242

Estimate of p-value=0.3373

Conclusion: Fail to reject H₀, the data may have come from an uniform distribution (since P-value>0.05)