We want to examine if there is a linear relationship between X (math test score)
ID: 3309872 • Letter: W
Question
We want to examine if there is a linear relationship between X (math test score) and Y (physics test score) with 10 students. Using the data are listed below, we want to calculate the Pearson correlation coefficient. Then we will test if the correlation coefficient you calculated using the sample is statistically significant. Fill in the cells first.
Calculate the Pearson correlation coefficient.
Is the linear relationship between math scores and physics scores significant? Answer the question using the four steps of hypothesis testing.
Type in the data in SPSS data window. Analyze the relationship between the two variables using SPSS. Copy and paste the output. Is the p-value smaller than 0.05? Is the conclusion you made using the p-value consistent with the conclusion you made using the observed and critical values in Question 2?
ID X Y 1 2 3 2 3 6 3 4 6 4 5 7 5 8 7 6 5 7 7 6 7 8 8 8 9 7 11 10 12 11Explanation / Answer
SPSS Output:
Correlations
x
y
x
Pearson Correlation
1.000
.827**
Sig. (2-tailed)
.003
N
10
10
y
Pearson Correlation
.827**
1.000
Sig. (2-tailed)
.003
N
10
10
**. Correlation is significant at the 0.01 level (2-tailed).
The value of the correlation is 0.827
H0: The value of the correlation is insignificant
H1: The value of the correlation is significant
Level of significance is 0.05
r = 0.827
p-value = .003
Here the p-value is less than the level of significance (.003<.05)
The null hypothesis can be rejected at 5% level of significance.
We can conclude that linear relationship between math scores and physics scores is significant
Correlations
x
y
x
Pearson Correlation
1.000
.827**
Sig. (2-tailed)
.003
N
10
10
y
Pearson Correlation
.827**
1.000
Sig. (2-tailed)
.003
N
10
10
**. Correlation is significant at the 0.01 level (2-tailed).
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