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 |
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(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
To test :
Test statistic :
where , and
Degrees of freedom = 22
We reject the null hypothesis or H0 if the observed value of , where ,
The value of the test statistic :
Critical value :
Now ,
Hence we reject the null hypothesis or H0 .
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.
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