Question

A market research firm used a sample of individuals (32 persons) to rate the purchase potential of a particular product before and after the individuals saw a new television commercial about the product.

Use α=0.05 and the following data to test the hypothesis and comment on the value of the commercial. Please refer to table below and make the following decisions:

	Before	After
Mean	16,121875	15,40813
Variance	60,7546996	51,37904
Observation	32	32
Person Correlation	0,93584894
Hypothesized Mean Difference	0
df	31
t Stat	1,46836098
P(T<=t) one-tail	0,07604045
t Critical one-tail	1,69551878
P(T<=t) two-tail	0,15208089
t Critical two-tail	2,03951345

1. Set up the null and alternative hypothesis for testing whether there is a difference between situation before and after. Is this independent sample or paired sample? Why?
2. Provide the standard deviation for Sample 1 (Before)
3. Given the hypothesis in (a) would you reject Ho? (Note the significance level of 5%). Please provide short explanation why you reject or do not reject Ho. What is the p-value and what is your conclusion?
4. You would like to reject null hypothesis. At α=2 level of significance, what is your conclusion? Why?
5. What could be the highest confidence of conclusion that purchase potential of a particular product is significantly different before and after the individuals saw a new television commercial about the product?

Answer 1

(1)

Question:

Set up the null and alternative hypothesis for testing whether there is a difference between situation before and after. Is this independent sample or paired sample? Why?

H0: Null Hypothesis: = 0 (There is no difference between situation before and after the individuals saw a new television commercial about the product)

HA: Alternative Hypothesis: 0 (There is a difference between situation before and after the individuals saw a new television commercial about the product) (Claim)

This is paired sample because the 2 samples are not independent.The sample is measured twice: before and after the individuals saw a new television commercial about the product.

(2)

Question:

Provide the standard deviation for Sample 1 (Before)

the standard deviation for Sample 1 (Before) =

(3)

Question:

Given the hypothesis in (a) would you reject Ho? (Note the significance level of 5%). Please provide short explanation why you reject or do not reject Ho. What is the p-value and what is your conclusion?

t Stat = 1,46836098

ndf = 32 - 1 = 31

Two Tail Test

By Technology, P - Value = 0.15207

Since P - Value = 0.15207 is greater than = 0.05, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data do not support the claim that there is a difference between situation before and after the individuals saw a new television commercial about the product.

(4)

Question:

At α=2% level of significance, what is your conclusion? Why?

Since P - Value = 0.15207 is greater than = 0.02, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data do not support the claim that there is a difference between situation before and after the individuals saw a new television commercial about the product.

(5)

Question:

What could be the highest confidence of conclusion that purchase potential of a particular product is significantly different before and after the individuals saw a new television commercial about the product?

the highest confidence of conclusion = (1 - 0.15207) X 100 = 84.793 %