Question

A professor in the school of business at a certain university wants to investigate the claim that the prices of new textbooks in the campus store are higher than a competing national online bookstore by more than 50 cents. The professor randomly chooses required texts for 12 business school courses. Use α=0.05α=0.05. The data is given in the table below.

Book	Campus Store	Online Store
A	108.51	109.42
B	200.06	201.93
C	223.52	226.39
D	186.12	183.9
E	121.65	122.13
F	69.01	69.75
G	126.3	126.79
H	120.63	122.32
I	63.11	63.49
J	107.43	108.76
K	162.07	158.02
L	144.9	140.08

(a) Let XAXA denote the price of books at the campus store, and XBXB be the price of books at the online store, also let XD=XA−XBXD=XA−XB. Choose the correct statistical hypotheses.
A. H0:μD~>0.5,HA:μD~<0.5H0:μD~>0.5,HA:μD~<0.5
B. H0:μ~campus=μ~online,HA:μ~campus≠μ~onlineH0:μ~campus=μ~online,HA:μ~campus≠μ~online
C. H0:μcampus=μonline,HA:μcampus≠μonlineH0:μcampus=μonline,HA:μcampus≠μonline
D. H0:μD~=0.5,HA:μD~<0.5H0:μD~=0.5,HA:μD~<0.5
E. H0:μ~campus=μ~online,HA:μ~campus<μ~onlineH0:μ~campus=μ~online,HA:μ~campus<μ~online
F. H0:μD=0.5HA:μD>0.5H0:μD=0.5HA:μD>0.5
G. H0:μD>0.5,HA:μD<0.5H0:μD>0.5,HA:μD<0.5
H. H0:μcampus=μonline,HA:μcampus<μonlineH0:μcampus=μonline,HA:μcampus<μonline
I. H0:μD~=0.5,HA:μD~≠0.5H0:μD~=0.5,HA:μD~≠0.5
J. H0:μD~=0.5HA:μD~>0.5H0:μD~=0.5HA:μD~>0.5
K. H0:μcampus=μonline,HA:μcampus>μonlineH0:μcampus=μonline,HA:μcampus>μonline
L. H0:μ~campus=μ~online,HA:μ~campus>μ~onlineH0:μ~campus=μ~online,HA:μ~campus>μ~online


(b) Carry out the appropriate statistical test and find the P-value, to at least three decimal places.
P=

(c) Based on the above calculations, we should reject or not reject  the null hypothesis.

(d) Using the technology available to you, create the most appropriate graph(s) to check the assumption(s) that need to be satisfied for your inferences in (b) and (c) to be valid. What statement below aligns with your findings?
A. The prices charged at the campus bookstore are normally distributed.
B. The prices charged at the campus bookstore are not normally distributed.
C. The differences in the price of a textbook at the campus bookstore and the price of the textbook at the online store are not normally distributed.
D. The prices charged at the online bookstore are not normally distributed.
E. The differences in the price of a textbook at the campus bookstore and the price of the textbook at the online store are normally distributed.
F. The prices charged at the online bookstore are normally distributed.

Answer 1

(a) Claim: The prices of new textbooks in the campus store are higher than a competing national online bookstore by more than 50 cents that is

The claim comes under the alternative hypothesis.

Option F is correct for null and alternative hypothesis.

H0:μD=0.5 HA:μD>0.5

(b) t-test for paired difference.

The differences of campus store and online store are -0.91, -1.87, -2.87, 2.22, -0.48, -0.74, -0.49, -1.69, -0.38, -1.33, 4.05, 4.82

The mean and standard deviations of the differences are,

The formula of t-test statistics,

Degrees of freedom = n - 1 = 12 - 1 = 11

The alternative hypothesis contains the greater than sign so the test is a right-tailed test.

The P-value for the right-tailed test using excel is

=t.dist.rt(test statistics, DF) = t.dist.rt(-0.68, 11) is 0.744719

P-value = 0.745

(c) Alpha = 0.05

Decision rule: If P-value > alpha then fail to reject the null hypothesis otherwise reject the null hypothesis.

P-value (0.745) > alpha (0.05) so fail to reject the null hypothesis.

Conclusion: There is no sufficient evidence to support the claim that the prices of new textbooks in the campus store are higher than a competing national online bookstore by more than 50 cents.

(d) Using the graph of differences, the differences are normally distributed.

Option E is correct.

The differences in the price of a textbook at the campus bookstore and the price of the textbook at the online store are normally distributed.