A furniture manufacturer produces tables and chairs. A sample of 80 tables is te

Question

A furniture manufacturer produces tables and chairs. A sample of 80 tables is tested and 7 are found to be not up to specification. A sample of 90 chairs were tested and 14 did not meet specifications. Test whether there is a difference between proportion with significance.91 level A furniture manufacturer produces tables and chairs. A sample of 80 tables is tested and 7 are found to be not up to specification. A sample of 90 chairs were tested and 14 did not meet specifications. Test whether there is a difference between proportion with significance.91 level

Explanation / Answer

Given that,
sample one, x1 =7, n1 =80, p1= x1/n1=0.088
sample two, x2 =14, n2 =90, p2= x2/n2=0.156
null, Ho: p1 = p2
alternate, H1: p1 != p2
level of significance, = 0.91
from standard normal table, two tailed z /2 =0.113
since our test is two-tailed
reject Ho, if zo < -0.113 OR if zo > 0.113
we use test statistic (z) = (p1-p2)/(p^q^(1/n1+1/n2))
zo =(0.088-0.156)/sqrt((0.124*0.876(1/80+1/90))
zo =-1.346
| zo | =1.346
critical value
the value of |z | at los 0.91% is 0.113
we got |zo| =1.346 & | z | =0.113
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -1.346 ) = 0.1783
hence value of p0.91 > 0.1783,here we reject Ho
ANSWERS
---------------
null, Ho: p1 = p2
alternate, H1: p1 != p2
test statistic: -1.346
critical value: -0.113 , 0.113
decision: reject Ho
p-value: 0.1783
we have enough evidence to support the claim that difference between proportion

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