# Answer to Question #3137 in Statistics and Probability for Nia locus

Question #3137

Music No Music
17 17
16 18
15 17
16 17
18 19
18 18
a. What statistical test should be used to analyze the data?
b. Is this a one- or two tailed test?
c. Identify H0 and Ha for this study.
d. Conduct the appropriate analysis. Should H0 be rejected? What should the researcher conclude?
e. Calculate the 95 confidence interval.

Expert's answer

a. What statistical test should be used to analyze the data?

Paired T-test

b. Is this a one- or two tailed test?

Two tailed test

c. Identify H0 and Ha for this study.

H0: ud=0

Ha: ud≠0

d. Conduct the appropriate analysis. Should H0 be rejected?

What should the researcher conclude?

Statistic = d-bar/(sd/√n)

Music No Music (difference d)

17 17 0

16 18 -2

15 17 -2

16 17 -1

18 19 -1

18 18 0

n= 6

d-bar= -1

sd=0.8944

t-Statistic=-1/(0.8944/√6)=-2.739

Taking α=0.05

Critical values are: -t(0.025,5)=-2.571 and t(0.025,5)=2.571

We reject H0 since -2.739 <-2.571

Also we may calculate the 95 confidence interval.

95% CI for the difference is: d-bar±t(0.025,5)sd/√n =-1±2.571(0.8944/√6)

CI = (-1.939,-0.061)

Paired T-test

b. Is this a one- or two tailed test?

Two tailed test

c. Identify H0 and Ha for this study.

H0: ud=0

Ha: ud≠0

d. Conduct the appropriate analysis. Should H0 be rejected?

What should the researcher conclude?

Statistic = d-bar/(sd/√n)

Music No Music (difference d)

17 17 0

16 18 -2

15 17 -2

16 17 -1

18 19 -1

18 18 0

n= 6

d-bar= -1

sd=0.8944

t-Statistic=-1/(0.8944/√6)=-2.739

Taking α=0.05

Critical values are: -t(0.025,5)=-2.571 and t(0.025,5)=2.571

We reject H0 since -2.739 <-2.571

Also we may calculate the 95 confidence interval.

95% CI for the difference is: d-bar±t(0.025,5)sd/√n =-1±2.571(0.8944/√6)

CI = (-1.939,-0.061)

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