Q1) P-value =0.04252
Q2) 95% confidence interval for the change
=(0.0018 ,0.0464)
Solution:
For 2005 x1 = 333 n1=1771 p1=333/1771=0.188029
For 1988 x2=480 n2=2928, p2= 480/2928=0.163934
p-hat = ( x1 + x2) / ( n1 + n2). = (333+480)/(1771+2928)
=0.173016
Here Null and alternative hypothesis are below:
H0 : p1=p2
H1: p1 > p2
To calculate we first need to calculate test statistics z and
then calculate p(Z>z)
Test statistics z=(p1-p2)/sqrt(p-hat*(1-p-hat)*(1/n1+1/n2
z=(0.188029-
0.163934)/sqrt(0.173016*(1-0.173016)*((1/1771)+(1/2928)))
=2.1160
P-Value
For Ha: p1 - p2 > 0, we calculate the
proportion of the normal distribution that is greater than
Z.
i.e p(Z> 2.1160)=0.04252
P-value =0.04252
appropriate confidence interval
95% Confidence interval
((p1-p2) - Z_alpha*sqrt(p-hat*(1-p-hat)*(1/n1+1/n2,(p1-p2) +
Z_alpha*sqrt(p-hat*(1-p-hat)*(1/n1+1/n2)
at alpha=0.05Â Â Z_alpha=1.96
CI= ((0.188029-
0.163934)-1.96*sqrt(0.173016*(1-0.173016)*((1/1771)+(1/2928))),(0.188029-
0.163934)+1.96*sqrt(0.173016*(1-0.173016)*((1/1771)+(1/2928))))
=(0.0018 ,0.0464)
95% confidence interval for the change
=(0.0018 ,0.0464)
