Question

A researcher thinks that listening to classical music reduces anxiety. She measures the anxiety of 10 persons then plays Mozart's "Eine Kleine Nachtmusik". Following that the researcher measures their anxiety again. (Note that anxiety is measured on a scale from 1 to 7, with higher numbers indicating increased anxiety.)

Does the study support her hypothesis? Compute the upper bound of the confidence interval using the following data:

mean of the difference scores (subtract pretest from posttest): -1.6

standard error of the difference scores: 0.4

The formula for the CI upper bound is [standard error of the difference scores]*[t critical value]+[mean of the difference scores]

How do you find the t critical value? and what is the value for the upper bound?

Answer 1

Here we need to determine whether listening to classical music reduces anxiety

So., the hypothesis can be built as follows

Null Ho: mean anxiety classical = mean anxiety

Alternative Ha:  mean anxiety classical < mean anxiety

Now we have found the mean difference of sample as = -1.6 with 0.4 as std deviation

So., t=-1.6/0.4 =-4

& CI upper bound=[standard error of the difference scores]*[t critical value]+[mean of the difference scores] = 0.4* t ck + (-1.6)

Now to calculate the critical values we need to look at the t distribution for 5% area under the curve of the lower tail at n-1=9 degrees of freedom

So from the t table we get the tck=-1.833113

So., the t value for the acceptance region is -1.833113 to +inf

Soince the Accceptance region for Ho is  -1.833113 to +inf while   the t value here is -4 we need to reject the Ho and hence we conclude that  classical music reduces anxiety.

So., upper bound=0.4* t ck + (-1.6) = 0.4* -1.833113 + (-1.6) =-2.333245

Hope the above answer has helped you in understanding the problem. Please upvote the ans if it has really helped you. Good Luck!!