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" for them. Following that researcher measures their anxiety again.

Consider the research design described above. 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): -1.9

Standard error of the difference scores: 0.6

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

Answers must be expressed as a decimal out to 2 places. (e.g., .20)

PART 2

Would you reject the null hypothesis given your response to the question above?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: μ(d) = 0
Alternative Hypothesis: μ(d) < 0

sample mean, xbar = -1.9
sample standard deviation, s = 0.6
sample size, n = 10
degrees of freedom, df = n - 1 = 9

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.262

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (-1.9 - 2.262 * 0.6/sqrt(10) , -1.9 + 2.262 * 0.6/sqrt(10))
CI = (-2.33 , -1.47)

As the calculated does not include 0, we reject the null hypothesis.