According to a study by the American Pet Food Dealers Association, 61% of U.S. h
ID: 3310201 • Letter: A
Question
According to a study by the American Pet Food Dealers Association, 61% of U.S. households own pets. A report is being prepared for an editorial in the San Francisco Chronicle. As a part of the editorial a random sample of 260 households showed 170 own pets. Does this data disagree with the Pet Food Dealers Association data? Use a 0.05 level of significance.
(A) State the null hypothesis and the alternative hypothesis.
H0: =
H1:
(b)State the decision rule for 0.05 significance level (Negative value should be indicated by a minus sign. Round your answers to 2 decimal places.)
H0 is rejected if z is not between ( ) and ( ) .
(C) Compute the value of the test statistic. (Round your answer to 2 decimal places.)
Value of the test statistic:
(d)Does this data disagree with the Pet Food Dealers Association data? Use a 0.05 level of significance.
H0 is (Rejected/not rejected). There is (sufficient/insufficient) evidence to show the proportion has changed.
Explanation / Answer
Given that,
possibile chances (x)=170
sample size(n)=260
success rate ( p )= x/n = 0.6538
success probability,( po )=0.61
failure probability,( qo) = 0.39
null, Ho:p=0.61
alternate, H1: p!=0.61
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.65385-0.61/(sqrt(0.2379)/260)
zo =1.4495
| zo | =1.4495
critical value
the value of |z | at los 0.05% is 1.96
we got |zo| =1.45 & | z | =1.96
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 1.44951 ) = 0.1472
hence value of p0.05 < 0.1472,here we do not reject Ho
ANSWERS
---------------
null, Ho:p=0.61
alternate, H1: p!=0.61
test statistic: 1.4495
critical value: -1.96 , 1.96
decision: do not reject Ho
p-value: 0.1472
no we don't disagree with the Pet Food Dealers Association data
do not reject Ho
There is insufficient evidence to show the proportion has changed.
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