please answer number 25 a b c d e f g h 1500 points givenSol

please answer number 25 a b c d e f g h

1500 points given.

Solution

(a) Let p be the population proprtion

Null hypothesis : p=8/9

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(b) Alternative hypothesis: p not equal to 8/9

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(c) We use Z test

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(d) The probability is

P(X=8)=0.018

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(e) The probability is

P(X>=8) = P(X=8)+P(X=9) =0.018+0.002 =0.02

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(f) The test statistic is

Z=(phat-p)/sqrt(p*(1-p)/n)

=(0.018-8/9)/sqrt((8/9)*(1/9)/9)

=-8.31

It is a two-tailed test.

So the p-value= 2*P(Z<-8.31) =0 (from standard normal table)

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(g) Since the p-value is less than 0.05, we reject the null hyothesis.

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(h)If we calculate a 95% confidence interval for the true proportion of correct identifications, we have 95% confident that the true proportion of correct identifications will be within this interval.