Question

A group says that the mean daily lodging cost for a family traveling in Region 1...

A group says that the mean daily lodging cost for a family traveling in Region 1 is the same as in Region 2. The mean daily lodging cost for

3939

families traveling in Region 1 is

​\$141141

with a population standard deviation of

​\$2424.

The mean daily lodging cost for

3939

families traveling in Region 2 is

​\$135135

with a population standard deviation of

​\$2525.

At

alpha equals 0.10 commaα=0.10,

is there enough evidence to reject the​ group's claim? Complete parts​ (a) through​ (e).​(a) Identify the claim and state

Upper H 0H0

and

Upper H Subscript aHa.

What is the​ claim?

A.

The mean daily lodging costs in Region 1 and Region 2 are different.

B.

The mean daily lodging costs in Region 1 and Region 2 are equal.

C.

The mean daily lodging cost in Region 1 is less than Region 2.

D.

The mean daily lodging cost in Region 1 is greater than Region 2.

What are

Upper H 0H0

and

Upper H Subscript aHa​?

A.

Upper H 0H0​:

mu 1μ1less than<mu 2μ2

Upper H Subscript aHa​:

mu 1μ1greater than or equals≥mu 2μ2

B.

Upper H 0H0​:

mu 1μ1less than or equals≤mu 2μ2

Upper H Subscript aHa​:

mu 1μ1greater than>mu 2μ2

C.

Upper H 0H0​:

mu 1μ1not equals≠mu 2μ2

Upper H Subscript aHa​:

mu 1μ1equals=mu 2μ2

D.

Upper H 0H0​:

mu 1μ1greater than or equals≥mu 2μ2

Upper H Subscript aHa​:

mu 1μ1less than<mu 2μ2

E.

Upper H 0H0​:

mu 1μ1equals=mu 2μ2

Upper H Subscript aHa​:

mu 1μ1not equals≠mu 2μ2

F.

Upper H 0H0​:

mu 1μ1greater than>mu 2μ2

Upper H Subscript aHa​:

mu 1μ1less than or equals≤mu 2μ2

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

The critical​ value(s) is/are

nothing.

​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.)

What​ is/are the rejection​ region(s)?

A.

zgreater than>2.575

B.

zless than<​1.28,

zgreater than>1.28

C.

zgreater than>minus−2.33

D.

zless than<minus−​2.33,

zgreater than>2.33

E.

zless than<minus−​2.575,

zgreater than>2.575

F.

zless than<1.645

G.

zless than<minus−​1.645,

zgreater than>1.645

H.

zless than<1.28

​(c) Find the standardized test statistic z for

mu 1μ1minus−mu 2μ2.

zequals=nothing

​(Round to three decimal places as​ needed.)

​(d) Decide whether to reject or fail to reject the null hypothesis. Choose the correct answer below.

A.

RejectReject

Upper H 0H0.

The standardized test statistic

is notis not

in the rejection region.

B.

Fail to rejectFail to reject

Upper H 0H0.

The standardized test statistic

is notis not

in the rejection region.

C.

RejectReject

Upper H 0H0.

The standardized test statistic

isis

in the rejection region.

D.

Fail to rejectFail to reject

Upper H 0H0.

The standardized test statistic

isis

in the rejection region.

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

At the

nothing​%

significance​ level, there is

insufficient

sufficient

evidence to

reject

support

the claim that the mean daily lodging costs in Region 1 is

less than

equal to

different from

greater than

the mean daily lodging costs in Region 2.