Question

1. A researcher asks whether people will score higher on a questionnaire measuring well-being when they are exposed to lots of sunshine compared to when they’re not exposed to lower levels of sunshine. A sample of 8 people is first measured after low levels of sunshine exposure and then again after high levels of exposure.  The researcher collects the well-being scores given below.  What should the researcher conclude about these results, α =.01?

Low:    14        13        17        15        18        17        14        16

High:   18        12        20        19        22        19        19        16

1. Test the hypothesis using the 5-step method. (18 points)
2. Calculate the 99% confidence interval. (4 points)
3. Calculate and estimate the effect size. (4 points)

(This is t-test for psychology statistics)

Answer 1

Ans:

	Before	after	d
1	14	18	4
2	13	12	-1
3	17	20	3
4	15	19	4
5	18	22	4
6	17	19	2
7	14	19	5
8	16	16	0
		d-bar	2.625
		sd	2.1339

a)

Test statistic:

t=(2.625-0)/(2.1339/sqrt(8))

t=3.479

df=8-1=7

p-value=tdist(3.479,7,1)=0.0051

As,p-value<0.01,reject the null hypothesis.

There is sufficient evidence to conclude that people will score higher on a questionnaire measuring well-being when they are exposed to lots of sunshine.

b)

t*=tinv(0.01,7)=3.499

99% confidence interval for mean difference

=2.625+/-3.499*(2.1339/sqrt(8))

=2.625+/-2.640

=(-0.015, 5.265)

c)

Effect size,r^2=2.625^2/(2.625^2+7)=0.496