Question

A researcher was interested in investigating if younger women feel more positively toward themselves than older women. She obtains the cooperation of five mother-daughter pairs. The daughters are all college students. She then administers a measure of self-esteem to these ten women. The scores range from zero to ten with ten meaning high self-esteem. The scores are as follows:

Mother-Daughter Pair	Mother	Daughter
1	4	6
2	10	10
3	6	8
4	9	7
5	6	9

1. State the null and research hypotheses.

2. Find the Critical Value using the T-Table and interpret what you will do with the null hypothesis given that Critical Value

3. Identify the Correct Degrees of Freedom you’ll use in the table

4. Calculate the t-value. Show your work. Start with the formula and then plug in the correct values from there.

5. Make a decision regarding the null. Interpret your decision with regard to this question.

6. Calculate the effect size and interpret what it means.

7. Construct a 95% Confidence Interval for the difference between the two groups.

8. Reflect on the results and the exercise (summarize the results).

Answer 1

(1)

H0: Null Hypothesis:

HA: Alternative Hypothesis:

(2)

= 0.05

ndf = n - 1 = 5 - 1= 4

One Tail Left Side Test

From Table, critical value of t = - 2.1318

Decision Rule:

Reject null hypothesis: if t < - 2.1318

(3)

Degrees of freedom is given by:

ndf = n - 1 = 5 - 1= 4

(4)

From the given data,values of d = Mother - Daughter are got as follows:

d = - 2, 0, - 2, 2, - 3

From d values,the following statistics are calculated:

n = 5

= -5/5 = - 1

s_d = 2

SE = s_d/

= 2/

=0.8944

Test statistic is given by:

t = /SE

   = - 1/0.8944

= - 1.1180

(5)

Since calculated value of t = - 1.1180 is greater than critical value of t = - 2.1318, the difference is not significant. Fail to reject null hypothesis.

Conclusion:

The data do not support the claim that younger women feel more positively toward themselves than older women.

(6)

Effect size : Cohen's d for Dependent Samples t test:

From the given data, the following statistics are calculated:

m₁= 7

s₁ = 2.4495

m₂ = 8

s₂ = 1.5811

r = 0.5809

Substituting values, we get:

So,

Effect size = 0.500

Interpretation:

Since Effect size = 0.5, the effect is medium.

(7)

ndf =4

=0.05

From Table,

critical values of t = 2.7764

Confidence interval:

- 1 (2.7764 X 0.8944)

= - 1 2.4832

= ( - 3.4832,1.4832)

Confidence Interval:

- 3.4832 < < 1.4832

(8)

Since the confidence interval contains 0, we conclude:

The data do not support the claim that younger women feel more positively toward themselves than older women.