Calculate the test statistic and pvalue for each sample Use

Calculate the test statistic and p-value for each sample. Use Appendix C-2 to calculate the p-value. (Negative values should be indicated by a minus sign. Round your test statistic to 3 decimal places and p-value to 4 decimal places.)

Solution

(a) The test statistic is

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

=(43/82-0.45)/sqrt(0.45*(1-0.45)/82)

=1.354

So the p-value= P(Z>1.354)=0.0879 (from standard normal table)

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(b)The test statistic is

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

=(17/38-0.3)/sqrt(0.3*0.7/38)

=1.982

So the p-value= 2*P(Z>1.982)=0.0475 (from standard normal table)

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(c)The test statistic is

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

=(6/103-0.1)/sqrt(0.1*0.9/103)

=-1.412

So the p-value= P(Z<-1.412)=0.0790 (from standard normal table)