A random sample consists of eight tax filers who completed their tax forms on th

Question

A random sample consists of eight tax filers who completed their tax forms on their own. Their forms were found to have 1, 3, 2, 4, 0, 2, 1, and 2 mistakes, respectively. Determine the 90% confidence interval for the mean number of mistakes that a tax filer will make in his/her forms if they're completed on his/her own. Assume the distribution of the number of mistakes in tax forms is approximately normal. A random sample of size 90 yields a sample proportion 0.3. (a) Is the sample size large enough to construct a large-sample confidence interval for p? (b) Construct a 99% confidence interval for p.

Explanation / Answer

here for 7 degree of freedom and 90% CI, t=1.8946

hence confidence interval =mean +/- t*std error =1.040 ; 2.710

b)here np=90*0.3=27>10 and npq=>10 hence it fullfill the requirement

here p =0.3

and std error =(p(1-p)/n)1/2 =0.0483

and for 99% CI, z=2.5758

hence confidence interval =P+/- z*std error =0.1756 ; 0.4244

X 1.000 3.000 2.000 4.000 0.000 2.000 1.000 2.000 mean(X) 1.875 std deviation(S) 1.246 std error =S/(n)1/2 0.441

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