A researcher was interested in whether people who know more about a product woul

Question

A researcher was interested in whether people who know more about a product would be more satisfied with the product. The researcher administered a satisfaction test about the product to 8 people, then showed a video explaining the product and re-administered the same satisfaction test. The before and after scores are listed in the table below, with higher scores indicating higher satisfaction. Conduct a t-test for dependent means at the .05 level of significance.

Subject After Before
A 8.5 8.4
B 4.3 4.6
C 2.0 1.7
D 7.8 7.3
E 7.0 7.2
F 9.1 7.4
G 3.3 3.0
H 3.5 3.5

Use the information from the table above to answer the questions in the boxes below. Be sure to show all calculations along with your answers.


1) State your research hypothesis. Is it directional or nondirectional? (2 points) Answer below: .

AND
2) State your null hypothesis. (1 point) Answer below: .

AND
3) What is the mean of the difference scores? (1 point) Answer below: .

AND
4) What are the degrees of freedom (df)? (1 point) Answer below: .

AND
5) What is the estimate of the population variance from the sample? (1 point) Answer below: .

AND
6) What is the variance of the distribution of differences? (1 point) Answer below: .

AND
7) What is the standard deviation of the distribution of differences (standard error)? (2 points) Answer below: .

AND
8) What is the cut-off score at which the null hypothesis will be rejected (use t-table)? Is it a one-tailed or two-tailed test? Why? (2 points) Answer below: .

AND
9) What is the t-score of the sample mean? (2 points) Answer below: .

AND
10) What is your conclusion? State it in words and in symbols as you would for a research article. (2 points) Answer below: .

Explanation / Answer

1) State your research hypothesis. Is it directional or nondirectional? (2 points) Answer below: .

H0 : 1=2

H1 : otherwise

where 1 and 2 are the means of after and before respectively

This is a non directional hypothesis

AND
2) State your null hypothesis. (1 point) Answer below: .

H0 : 1=2

The mean of the scores before and after the video was shown are same

AND
3) What is the mean of the difference scores? (1 point) Answer below: .

The difference scores

0.1

-0.3

0.3

0.5

-0.2

1.7

0.2

0.0

The mean of the difference scores 0.2875

[ we could write our hypothesis in terms of this difference score as well, the hypothesis would be 

H0 :=0

H1 : otherwise

where  is the mean of the difference scores

AND
4) What are the degrees of freedom (df)? (1 point) Answer below: .

df is 8-1 =7

AND
5) What is the estimate of the population variance from the sample? (1 point) Answer below: .

estimate of the  population variance=2.666/7=0.3808

AND
6) What is the variance of the distribution of differences? (1 point) Answer below: .

variance of the distribution of differences (sample variance) =2.666/8=0.333

AND
7) What is the standard deviation of the distribution of differences (standard error)? (2 points) Answer below: .

(here the wording is a bit wrong, strictly speaking it should be written as distribution of mean of the differences)

standard error for mean of the differences =sqrt(0.3808)/sqrt(n)=0.2181, n=8

AND
8) What is the cut-off score at which the null hypothesis will be rejected (use t-table)? Is it a one-tailed or two-tailed test? Why? (2 points) Answer below: .

Its  a two tailed test, as its a non directional test. we are not testing if the mean is greater or lower than 0, we are testing is its different from 0.

at 5 % significance level the cut off for rejection of null hypothesis is 2.36

AND
9) What is the t-score of the sample mean? (2 points) Answer below: .

the t statistic =(sample mean-0)/std err=0.2875/0.2181=1.31

AND
10) What is your conclusion? State it in words and in symbols as you would for a research article. (2 points) Answer below: .

We fail to reject the nuill hypothesis of no difference in scores before and after showing the video

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