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. The professor randomly chooses required texts for 12 business school courses. The data is given in the table below.

Book Number	Campus Store	Online Store
Book 1	125.45	124.27
Book 2	88.37	86.21
Book 3	230.98	229.6
Book 4	151.8	153.02
Book 5	236.44	237.4
Book 6	86.54	87.1
Book 7	146.09	144.21
Book 8	155.13	154.21
Book 9	164.82	161.71
Book 10	215.04	216.31
Book 11	249.83	246.81
Book 12	221.46	220.09

(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,HA:μD≠0H0:μD=0,HA:μD≠0
B. H0:μcampus=μonline,HA:μcampus<μonlineH0:μcampus=μonline,HA:μcampus<μonline
C. H0:μD=0,HA:μD<0H0:μD=0,HA:μD<0
D. H0:μcampus=μonline,HA:μcampus>μonlineH0:μcampus=μonline,HA:μcampus>μonline
E. H0:μcampus=μonline,HA:μcampus≠μonlineH0:μcampus=μonline,HA:μcampus≠μonline
F. H0:μD=0,HA:μD<0H0:μD=0,HA:μD<0
G. H0:μD>0,HA:μD<0H0:μD>0,HA:μD<0
H. H0:μD=0HA:μD>0H0:μD=0HA:μD>0


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

(c) Based on the above calculations, we should  ? reject not reject  the null hypothesis. Use α=0.05

(d) Using the technology available to you,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 online bookstore are normally distributed.
B. 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.
C. The prices charged at the online bookstore are not normally distributed.
D. 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.
E. The prices charged at the campus bookstore are normally distributed.
F. The prices charged at the campus bookstore are not normally distributed.

Answer 1

(a) Option: H. H₀:μ_D=0 H_A:μ_D>0

(b)

t-Test: Paired Two Sample for Means
	Campus Store	Online Store
Mean	172.6625	171.745
Variance	3260.176148	3260.698155
Observations	12	12
Pearson Correlation	0.99962014
Hypothesized Mean Difference	0
df	11
t Stat	2.019436984
P(T<=t) one-tail	0.034241211
t Critical one-tail	1.795884819
P(T<=t) two-tail	0.068482422
t Critical two-tail	2.20098516

Test statistic=2.0194

P-value=0.0342

(c) Since P-value<0.05, so reject  the null hypothesis.

(d)

From above probability plot we see that the differences follow normal distribution hence

Option: B. 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.