To test his hypothesis that students who finish an test first get better grades,

Question

To test his hypothesis that students who finish an test first get better grades, a professor kept track of the order in which papers were handed in. Of the first 24 papers, 14 received a B or better compared with 8 of the last 28 papers handed in.

  Reject the null hypothesis if zcalc > .

Find the test statistic zcalc and p-value. (Do not round the intermediate calculations but round the proportions to 4 decimal places. Round your final answers to 4 decimal places.)

Explanation / Answer

Part-a-2

Null hypothesis H0: p1=p2

Alternative hypothesis Ha: p1 >p2

Here p1 and p2 are the true proportions of those who got papers first and last papers respectively.

We reject the null hypothesis z>1.28

Part-a-3

phat1=14/24=0.58

phat2=8/28=0.29

N1=24 and N2=28

X1=14 andX2=8

Pooled proportion p=(X1+X2)/(N1+N2)=(14+8)/(24+28)=0.42

Pooled Standard error SE=sqrt(p*(1-p)*(1/N1+1/N2))

=sqrt(0.42*(1-0.42)*(1/24+1/28))

=0.1373

So test statistic zcalc=(phat1-phat2)/SE

=(0.58-0.29)/ 0.1373

=2.1122

p-value=P(Z>2.1122)=0.0173 using excel function =1-NORMSDIST(2.1122)

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