Question

A magazine claims that the mean amount spent by a customer at Burger Stop is greater than the mean amount spent by a customer at Fry World. The results for samples of customer transactions for the two fast food restaurants are shown below. At

alphaαequals=0.05

can you support the​ magazine's claim? Assume the population variances are equal. Assume the samples are random and​ independent, and the populations are normally distributed. Complete parts​ (a) through​ (e) below.

Burger Stop	Fry World
x overbar 1 equals= ​$8.44	x overbar 2 equals= ​$7.81
s 1 equals= ​$0.72	s 2 equals= ​$0.66
n 1 equals= 13	n 2 equals= 11

​(a) Identify the claim and state

Upper H0

and

Upper H Subscript aHa.

Which is the correct claim​ below?

A.

​"The mean amount spent by a customer at Burger Stop is equal to the mean amount spent by a customer at Fry​ World."

B.

​"The mean amount spent by a customer at Burger Stop is not equal to the mean amount spent by a customer at Fry​ World."

C.

​"The mean amount spent by a customer at Fry World is greater than the mean amount spent by a customer at Burger​ Stop."

D.

​"The mean amount spent by a customer at Burger Stop is greater than the mean amount spent by a customer at Fry​ World."

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 H 0H0

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

Enter the critical​ value(s) below.

_______

​(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.

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

B.

t greater than t 0t>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

5 %

significance​ level,

(4)

______ enough evidence to support the claim of the magazine that the mean amount spent by customers at Burger World is greater than the mean amount spent by customers at Fry World.

Which of these options below are 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

To test :

$H_0:\mu_1=\mu_2 \ \ vs.\ \ H_1:\mu_1>\mu_2$

Test statistic :

12 Ho 1V2

where , and

8.44 . x2 7.81 . n 13 . n2-11 . S1 0.72 .89 0.66 x

(n 1-1)si + (n2-1)s2 = 0.6934

Degrees of freedom = 22

We reject the null hypothesis or H₀ if the observed value of
t t22 (a
, where ,
a-0.05

The value of the test statistic :
t-2.218

Critical value :  
t22 (a) = 1.717

Now , $t=2.218>1.717$

Hence we reject the null hypothesis or H_{0 .}

Thus we have sufficient evidence to support the claim that the mean amount spent by a customer at Burger Stop is greater than the mean amount spent by a customer at Fry​ World.