Question

A market research firm used a sample of individuals to rate the purchase potential of a particular product before
and after the individuals saw a new television commercial about the product. The purchase potential ratings were
based on a 0 to 10 scale, with higher values indicating a higher purchase potential. Test whether the commercial
improved the mean purchase potential rating. at the .10 level of significance.
Individual	After	Before
Carl Hall	6	5
Malcom Armstead	6	4
Ron Baker	8	7
Landry Shamet	4	3
Evan Wessel	3	4
Fred Van Vleet	9	8
Tekele Cotton	7	6
Cleanthony Early	5	6
State H0 and H1
Show the Excel Output

Answer 1

against

Since, the observations are taken on same individuals, we use the t-test: Paired Two Sample for Means option from the Data Analysis menu of the data tab.

EXCEL OUTPUT:

t-Test: Paired Two Sample for Means
	After	Before
Mean	6	5.375
Variance	4	2.839
Observations	8	8
Pearson Correlation	0.848
Hypothesized Mean Difference	0
df	7
t Stat	1.667
P(T<=t) one-tail	0.070
t Critical one-tail	1.415
P(T<=t) two-tail	0.140
t Critical two-tail	1.895

Since, the alternative is one sided, we look at the p-value for the one-tail test. p-value=0.07( < 0.1 ), hence, we reject the Null at 10% level of significance and conclude that the commercial improved the mean purchase potential rating.

Also, t_cal (=1.667) > t_tab (=1.415) , this also indicates the rejection of the Null.