A pet association claims that the mean annual cost of food for dogs and cats are

Question

A pet association claims that the mean annual cost of food for dogs and cats are the same. The results for samples for the two types of pets are shown below. At alphaequals=0.010.01, can you reject the pet association's claim? Assume the population variances are not equal. Assume the samples are random and independent, and the populations are normally distributed. Complete parts (a) through (e) below. Dogs Cats x overbar 1x1 equals= $ 256$256 x overbar 2x2 equals= $ 221$221 s 1s1 equals= $ 41$41 s 2s2 equals= $ 37$37 n 1n1 equals= 1515 n 2n2 equals= 99 (a) Identify the claim and state Upper H 0H0 and Upper H Subscript aHa. Which is the correct claim below? A. "The mean annual costs of food for dogs and cats are not equal." B. "The mean annual cost of food for dogs is greater than the cost for cats." C. "The mean annual cost of food for cats is greater than the cost for dogs." D. "The mean annual costs of food for dogs and cats are equal."

Explanation / Answer

Given that,
mean(x)=256
standard deviation , s.d1=41
number(n1)=15
y(mean)=221
standard deviation, s.d2 =37
number(n2)=9
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.01
from standard normal table, two tailed t /2 =3.355
since our test is two-tailed
reject Ho, if to < -3.355 OR if to > 3.355
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =256-221/sqrt((1681/15)+(1369/9))
to =2.1534
| to | =2.1534
critical value
the value of |t | with min (n1-1, n2-1) i.e 8 d.f is 3.355
we got |to| = 2.15338 & | t | = 3.355
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 2.1534 ) = 0.063
hence value of p0.01 < 0.063,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: 2.1534
critical value: -3.355 , 3.355
decision: do not reject Ho
p-value: 0.063

D. "The mean annual costs of food for dogs and cats are equal."

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