Question

A cognitive psychologist hypothesizes that word chunking improves language development. To investigate, the psychologist assesses a group of 4-year olds by asking them to recall as many words as they can starting with the letter "s". The psychologist then asks the parents to ensure their children practice word chunking for 30 minutes each day for two weeks. At the end of the two weeks, the psychologist assesses the same children by asking them to recall as many words starting with the letter "s" again. What can be concluded with an α of 0.05? The word recall data are below.

1nd	2nd
5 8 6 2 8 4 3 5	6 8 9 5 9 6 4 7

a) What is the appropriate test statistic?
---Select---naz-testOne-Sample t-testIndependent-Samples t-testRelated-Samples t-test

b)
Condition 1:
---Select---2nd assessmenttwo weekswords starting with "s"30 minutes1nd assessment
Condition 2:
---Select---2nd assessmenttwo weekswords starting with "s"30 minutes1nd assessment

c) Obtain/compute the appropriate values to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value =______ ; test statistic = __________
Decision: ---Select---Reject H0Fail to reject H0

d) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below.
[____ , _____ ]

e) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
d = _______;---Select---natrivial effectsmall effectmedium effectlarge effect
r² =____ ; ---Select---natrivial effectsmall effectmedium effectlarge effect

f) Make an interpretation based on the results.

Word chunking significantly impairs language development.

Word chunking significantly improves language development.

     Word chunking did not have a significant impact on language development.

Answer 1

We input this data set in MS Excel and use the "t-Test: Paired Two Sample for Means" option under Data > Data Analysis to carry out this test and answer the given questions. The screenshot of the data set and output is given below.


(a) Related-Samples t-test, since the experiment is carried out on the same set of children.
(b) words starting with "s", two weeks.
(c) Critical value = -1.8946, test statistic = -4.3333, decision = Reject H0.
(d) (-2.5117, -0.7383).
(e) d = mean difference/s.d. of difference = 1.5321 (or, -1.5321). large effect.
r² = d²/(d² + 4) = 0.3698, small effect.
(f) Word chunking significantly improves language development.

A B с D E F 1 1st 2nd t-Test: Paired Two Sample for Means 5 6 N 3 8 8 4 6 9 Mean 1st 2nd 5.125 6.75 4.696428571 3.357142857 5 2 5 6 8 9 8 8 7 4 6 0.872458807 8 3 4 0 9 5 7 7 Variance Observations Pearson Correlation Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail 10 11 12 -4.333333333 0.00171193 1.894578604 0.00342386 2.364624251 13 14 15 16 17