Don\'t solve by hand, only minitab Don\'t solve by hand, only minitab Don\'t sol

Question

Don't solve by hand, only minitab

Don't solve by hand, only minitab

Don't solve by hand, only minitab

Don't solve by hand, only minitab

Provide an appropriate response. 3) An observed frequency distribution is as follows: Number of successes 0 1 2 Frequency i) 47 98 55 with n-2 and p 1/2, use the binomial formula to find the a binomial distribution probability ii) Using the corresponding to each category of the table. for each category probabilities found in part find the frequency ii) Use a 0.05 level of significance to test the claim that the observed frequencies fit a binomial distribution for which n 2 and p 1

Explanation / Answer

(i) let x=number of success and x is binomial distribution with parameter n=2,p=1/2=0.5

P(X=x)=nCxpx(1-p)n-x

P(X=0)=2C0(0.5)0(1-0.5)2-0 =1*1*0.5*0.5=0.25 ( or using ms-excel=BINOMDIST(0,2,0.5,0))

P(X=1)=0.5 (  ( or using ms-excel=BINOMDIST(1,2,0.5,0))

P(X=2)=0.25 (  ( or using ms-excel=BINOMDIST(2,2,0.5,0))

(ii) Expected frequency=P(X=x)*N

here N=total frequecny=200

E(X=0)=P(X=0)*N=0.25*200=50

and similarly

(iii) here we use chi-square test to check observed frequency(O) and expected frequency (E) follow binomial distribution.

null hypothesis H0: observed frequency=expected frequency

alternate hypotheis H1:observed frequency is not = expected frequency

chi-square=SUM((O-E)2/E)=0.72 with k-1=3-1=2 df

k=number of class=3

critical chi-square=chi-square(0.05,2)=5.99 which is more than calculated chi-square=0.72,

so we fail to reject H0 and conclude that observed frequency(O) fit binomial distribution with n=2 and p=1/2

following calculation has been made for answering the question

number of success(x) 0 1 2 E(x)=E 50 100 50

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