Question

3. An experiment generated 1200 random numbers in the interval [0, 1] using a uniform distribution. Then several mathematical transformations were used to convert these numbers into a set of 1200 values between 0 and 9. Here is a frequency table of the digits in the dataset: 0 1 2 3 4 5 6 7 8 9 115 128 106 116 121 102 119 105 156 132 Run a statistical test to verify if these digit frequencies appear with equal probability. Explain why you support or not support an equal probability assertion. Show your work using R studio

Answer 1

This is a test of goodness of fit.

H0: All digits occur with probability 1/10

H1: All digits do not occur with probability 1/10

Chi square test statistic= 19.1, df = 9,

p-value = 0.02436

Since p value is less than .05, evidence is enough to reject the null H0 at 5% level.

R Program

chisq.test(c(115 ,128 ,106 ,116 ,121 ,102, 119 ,105 ,156 ,132),p=rep(1/10,10))

R OUTPUT

Chi-squared test for given probabilities

data: c(115, 128, 106, 116, 121, 102, 119, 105, 156, 132)
X-squared = 19.1, df = 9, p-value = 0.02436