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

alphaαequals=0.05

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 1 equals= $ 202		x overbar 2 equals= $ 167
s 1 equals= $ 40		s 2 equals= $ 36
n 1 equals= 17		n 2 equals= 14

​(a) Identify the claim and state

Upper H0

and

Upper H Subscript aHa.

Which is the correct claim​ below?

A.

​"The mean annual cost of food for cats is greater than the cost for​ dogs."

B.

​"The mean annual cost of food for dogs is greater than the cost for​ cats."

C.

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

D.

​"The mean annual costs of food for dogs and cats are not​ equal."

What are

Upper H0

and

Upper H Subscript aHa​?

The null​ hypothesis,

Upper H0​,

is

(1)

The alternative​ hypothesis,

Upper H Subscript aHa​,

is

(2)

Which hypothesis is the​ claim?

The alternative​ hypothesis, Upper H Subscript aHa

The null​ hypothesis, Upper H0

​(b) Find the critical​ value(s) and identify the rejection​ region(s).

Enter the critical​ value(s) below.

nothing

​(Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as​ needed.)

Select the correct rejection​ region(s) below.

A.

t greater than t 0t>t0

B.

negative t 0 less than t less than t 0−t0<t<t0

C.

t less than minus t 0 comma t greater than t 0t<−t0, t>t0

D.

t less than minus t 0t<−t0

​(c) Find the standardized test statistic.

tequals=_________

​(Type an integer or decimal rounded to three decimal places as​ needed.)

​(d) Decide whether to reject or fail to reject the null hypothesis.

(3)

the null hypothesis.

​(e) Interpret the decision in the context of the original claim.

At the

five percent

significance​ level,

(4)

enough evidence to reject the claim that the mean annual costs of food for dogs and cats are the same.

Which of the options below is correct?

(1)

mu 1 equals mu 2 .μ1=μ2.

mu 1 less than or equals mu 2 .μ1≤μ2.

mu 1 greater than or equals mu 2 .μ1≥μ2.

(2)

mu 1 not equals mu 2 .μ1≠μ2.

mu 1 greater than mu 2 .μ1>μ2.

mu 1 less than mu 2 .μ1<μ2.

(3)

Fail to reject

Reject

(4)

there is not

there is

Answer 1