10. -10 points DevoreStat9 9.E.507.XP My Notes Ask Your T It is thought that the
ID: 3313461 • Letter: 1
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10. -10 points DevoreStat9 9.E.507.XP My Notes Ask Your T It is thought that the front cover and the nature of the first question on mail surveys influence the response rate. An article tested this theory by experimenting with different cover designs. One cover was plain; the other used a picture of a skydiver. The researchers speculated that the return rate would be lower for the plain cover Cover Plain Skydiver Number Sent 204 218 Number Returned 101 109 Does this data support the researchers' hypothesis? Test the relevant hypotheses using -0.10 by first calculating a P-value. State the relevant hypotheses. (Use pl for the plain cover and P2 for the skydiver cover.) Ho: p1-p2 = 0 Ha P1 P2 0 Ha P1 P2 0 Mo: P1-P2=0 Ha P1 P2> 0 Mo: p1-p2 = 0 P1 -P2Explanation / Answer
Given that,
sample one, x1 =101, n1 =204, p1= x1/n1=0.495
sample two, x2 =109, n2 =218, p2= x2/n2=0.5
null, Ho: p1 = p2
alternate, H1: p1 < p2
level of significance, = 0.1
from standard normal table,left tailed z /2 =1.282
since our test is left-tailed
reject Ho, if zo < -1.282
we use test statistic (z) = (p1-p2)/(p^q^(1/n1+1/n2))
zo =(0.495-0.5)/sqrt((0.498*0.502(1/204+1/218))
zo =-0.101
| zo | =0.101
critical value
the value of |z | at los 0.1% is 1.282
we got |zo| =0.101 & | z | =1.282
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: left tail - Ha : ( p < -0.1006 ) = 0.45992
hence value of p0.1 < 0.45992,here we do not reject Ho
ANSWERS
---------------
null, Ho: p1 = p2
alternate, H1: p1 < p2
test statistic: -0.10
critical value: -1.282
p-value: 0.4550
decision: failed to reject Ho, the data does not suggest that the front cover and
the nature of the first question on mail serveys influence the response rate
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