A sports psychologist believes that amount of practice is related to performance
ID: 3294239 • Letter: A
Question
A sports psychologist believes that amount of practice is related to performance. She measures the hours of basketball free-throw practice time of several players, and then free-throw performance in a game. The data are as follows: Practice time 1 2 1 3 3 4 4 4 5, # of shots made 1 1 1 2 1 3 2 2 3
Test whether practice time is related to #of shots made using SPSS to conduct Person Correlation Coefficient. Use the information from the output to complete the hypothesis test. Be sure to turn in both your output file, and your answers to the following questions:
Step 1: Write the null and research hypotheses in words
Step 2: Find the critical value . Set alpha = .05
Step 3: Compute the appropriate test statistic (just insert the correlation you found with SPSS.
When using SPSS this time you will enter the data in separate columns. Put the X-variable in the VAR1 column and put the Y-variable in the VAR2 column. We do it this way because we have an X and Y value for each participant in our data.
To compute the correlation just select Analyze from the menu at the top, then select correlate. Choose the Bivariate option. Pearson’s correlation should be checked as the default.
can double check the answer with your own computation if you like.
Step 4: Make a decision about the null. Reject or Fail to Reject.
Conclusion: Describe the relationship between practice time and #of shots made.
Conclusion: Describe the relationship between practice time and #of shots made.
Explanation / Answer
Step 1:
The null and alternative hypotheses for this test are given as below:
Null hypothesis: H0: There is no any statistically significant relationship exists between the amount of practice and performance.
Alternative hypothesis: Ha: There is a statistically significant relationship exists between the amount of practice and performance.
H0 : = 0 Versus Ha: 0
This is a two tailed test.
Step 2:
Level of significance or alpha value for this test is given as 0.05 or 5%.
Degrees of freedom = n – 2
Where n is the number of pairs
We are given
Number of pairs = n = 9
So, degrees of freedom = 9 – 2 = 7
Critical value = 2.3646
(By using t-table)
Step 3:
Required SPSS output for this test is given as below:
Correlations
Practice time
Number of shots
Practice time
Pearson Correlation
1
.849**
Sig. (2-tailed)
.004
N
9
9
Number of shots
Pearson Correlation
.849**
1
Sig. (2-tailed)
.004
N
9
9
**. Correlation is significant at the 0.01 level (2-tailed).
The test statistic formula for this test is given as below:
t = r*sqrt(n – 2)/sqrt(1 – r^2)
t = 0.849*sqrt(7)/sqrt(1 - 0.849*0.849)
t = 4.25
Step 4:
P-value = 0.0038 or 0.004 approximately (by using t-table)
Alpha value = 0.05
P-value < alpha value
So, we reject the null hypothesis that there is no any statistically significant relationship exists between the amount of practice and performance.
There is sufficient evidence to conclude that there is a statistically significant relationship exists between the amount of practice and performance.
Correlations
Practice time
Number of shots
Practice time
Pearson Correlation
1
.849**
Sig. (2-tailed)
.004
N
9
9
Number of shots
Pearson Correlation
.849**
1
Sig. (2-tailed)
.004
N
9
9
**. Correlation is significant at the 0.01 level (2-tailed).
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