Please provide each step in the process to answer the problem. Please provider t

Question

Please provide each step in the process to answer the problem.
Please provider the hypothesis and null hypothesis if and when appropriate.



Use the following data to answer the 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. (Let 1 = rating after; and 2 = rating before).
Purchase Rating

Individual After Before
1 6 5
2 6 4
3 7 7
4 4 3
5 3 5
6 9 8
7 7 5
8 6 6


a. Formulate the hypotheses that can be used to determine whether there is evidence to show that the commercial improved the mean purchase potential rating.


b. Using alpha= 0.01 , and the critical value approach to test the hypotheses. Do you reject or accept the null hypothesis? What is your conclusion? Explain.

Explanation / Answer

2= Ratings Before customers saw the new television commercial

1= Ratings after customers saw the new television commercial

Thus d (difference)= 2-1; d will signify the rating differences before and after the tv commercial

The Null Hypothesis will be given by

H0:d=0

and the alternative hypothesis will be given by

Ha:d < 0

b) Individual          Before           After          Difference

          1                     5                 6                     -1

          2                     4                 6                     -2

          3                     7                 7                      0

          4                     3                 4                     -1

          5                     5                 3                      2

          6                     8                 9                     -1

          7                     5                 7                     -2

          8                     6                 6                      0

n=8;

mean= diff/n=-5/8=-0.625

s= 1.3025

Test Statistic: t= mean-hypothesized value/(s/n)

=-.625-0/(1.3025/8)

t=-1.35 df=7

According to the t table in my book, the p value is = .1095

If we compare this value to alpha=.01

The p value determined from the Test Statistic is larger than the alpha value

Thus, we fail to reject the null hypothesis at alpha=.01.

In conclusion, this means that at the significance of .01 there is no evidence that the tv commercial improve the mean purchase potential rating.

I hope this helped

Cheers!

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