Question

Do consumers spend more on a trip to Store A or Store​ B? Suppose researchers interested in this question collected a systematic sample from 85 Store A customers and 82 Store B customers by asking customers for their purchase amount as they left the stores. The data collected is summarized by the accompanying table. Suppose researchers decide to test the hypothesis that the means are equal. The degrees of freedom formula gives 164.33 Test the null hypothesis at 0.05

Store A   Store B   n 85 82 y 44 54 s 21 19

A. Identify the null and alternative hypotheses.

B.Compute the test statistic.

C.Find the​ P-value.

State the conclusion. Choose the correct answer below.

A. tReject the null hypothesis. There is not sufficient evidence that the means are not equal.

B. Reject the null hypothesis. There is sufficient evidence that the means are not equal.

C.

Fail to rejectFail to reject

the null hypothesis. There

is notis not

sufficient evidence that the means are not equal.

D. Fail to reject the null hypothesis. There is sufficient evidence that the means are not equal.

Answer 1

Given that,
mean(x)=44
standard deviation , s.d1=21
number(n1)=85
y(mean)=54
standard deviation, s.d2 =19
number(n2)=82
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =1.99
since our test is two-tailed
reject Ho, if to < -1.99 OR if to > 1.99
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =44-54/sqrt((441/85)+(361/82))
to =-3.23
| to | =3.23
critical value
the value of |t α| with min (n1-1, n2-1) i.e 81 d.f is 1.99
we got |to| = 3.22905 & | t α | = 1.99
make decision
hence value of | to | > | t α| and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -3.2291 ) = 0.002
hence value of p0.05 > 0.002,here we reject Ho
ANSWERS
---------------
A.
null, Ho: u1 = u2
alternate, H1: u1 != u2
B.
test statistic: -3.23
critical value: -1.99 , 1.99
decision: reject Ho
C.
p-value: 0.002
D.
we have enough evidence to support the claim that There is sufficient evidence that the means are not equal.