An experiment was conducted to test whether classical music helps with mathematical performance. To study this, participants (n=9) were given an algebra test. Half of the sample completed the test in a room with classical music playing while the other half completed it in a room with no sounds at all. After a brief rest, the two groups switched rooms and completed a slightly modified version of the algebra test. Thus, all participants experienced both conditions. The scores for the two conditions were then compared, showing that listening to classical music did help mathematical performance by an average of MD =2 points with SS =32. a. Calculate the estimated standard error.   b. Compute the t statistic and state the conclusion of these findings.

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An experiment was conducted to test whether classical music helps with mathematical performance. To study this, participants (n=9) were given an algebra test. Half of the sample completed the test in a room with classical music playing while the other half completed it in a room with no sounds at all. After a brief rest, the two groups switched rooms and completed a slightly modified version of the algebra test. Thus, all participants experienced both conditions. The scores for the two conditions were then compared, showing that listening to classical music did help mathematical performance by an average of MD =2 points with SS =32.

a. Calculate the estimated standard error.

 

b. Compute the t statistic and state the conclusion of these findings.

Expert Solution
Part a

State the hypotheses.

Statistics homework question answer, step 1, image 1

That is, there is no evidence to conclude that classical music helps with mathematical performance.

Statistics homework question answer, step 1, image 2

That is, there is evidence to conclude that classical music helps with mathematical performance.

Decision rule:

Statistics homework question answer, step 1, image 3

 

Obtain the degrees of degrees of freedom.

The degrees of freedom are obtained below:

From the information, given that there is a sample of 9 participants.

Statistics homework question answer, step 1, image 4

Use EXCEL Procedure for finding the critical value of t at the 0.01 significance level.

 

Follow the instruction to obtain the critical value:

 

  1. Open EXCEL
  2. Go to Formula bar.
  3. In formula bar enter the function as“=TINV”
  4. Enter the probability value as 0.01.
  5. Enter the degrees of freedom as 8.
  6. Click enter

 

EXCEL output:

 

From the EXCEL output, the critical value of t at the 0.01 significance level for two tailed test with the 8 degrees of freedom is 3.3554.

 

 

Obtain the value of the sample variance.

The value of the sample variance is obtained below:

From the information, given that .

Statistics homework question answer, step 1, image 5

Obtain the value of the standard error.

The value of the standard error is obtained below:

Statistics homework question answer, step 1, image 6

Thus, the value of the standard error is 0.6667.

 

 

 

 

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