For the following give the number of degrees of freedom that would be used in fi

Question

For the following give the number of degrees of freedom that would be used in finding a Chi Squared Goodness of Fit Test critical value; in every case there are 10 intervals: 1. Sample data of heights of undergraduate female students on TTU campus being normally distributed. a. Sample data of times between 911 calls reporting arésidential fire being exponentially distributed b. 1o I- c. Sample data of random numbers from Excel's RAND() function being uniformly distributed between 0 and 1·(The uniform distribution has equal probabilities over the entire range.) What effect does sample size have on the degrees of freedom in a Chi Squared Goodness of Fit test? 2.

Explanation / Answer

so in part(a)

Given distribution is normal, as there are two parameter (mu and sigma) we have to measure so here the degree of freedom = (n-1) - number of parameters to calculate = (10 -1) -2 = 7

(b) In part, in exponential distribution, we only have to measure lambda, only one parameter so here the degree of freedom = (n-1) - parameters number = (10 - 1) - 1 = 8

(c) Here the distibution is uniform, number of parameters is one only, as in uniform distribution , we want to know only 1/(b-a) only

so Here degree of freedom = 10 -1 -1 = 8

Note : Weibull distribution has 3 parameters so in that case, degree of freedom = 10 -3 - 1= 6

Type of distribution No of constraints Degree of freedom Binominal distribution 1 n-1 Poisson/exponential distribution 2 n-2 Normal distribution 3 n-3

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