Question

A teacher gives a reading skills test to a third-grade class of n = 41 children at the beginning of the school year. To evaluate the changes that occur during the year, students are tested again at the end of the year. Their test scores showed an average improvement of M_D =4.9 points with s ² = 82.

A. Are the results sufficient to conclude that there is significant improvement in children’s reading skills? Use a one-tailed test with α = .01.

B. If there is a significant effect, compute Cohen’s d to measure the size of the effect.

C. Write a conclusion demonstrating how the outcome of the hypothesis test and the measure of effect size would appear in a research report in APA style.

Note: show all steps of hypothesis testing (i.e., write hypotheses, all computations, the t_critical, the decision about H₀ and the conclusion in APA reporting format).

Please explain in detail, thank you!

Answer 1

Answer:

Given,

n = 41

MD = 4.9

sd = sqrt(82)

α = .01

Here null hypothesis

Ho : d = 0

Alternative hypothesis

H1 : d > 0

Consider,

Upper tailed test = d / (sd/sqrt(n))

= 4.9 / sqrt(82)/sqrt(41)

= 3.4648

Now degree of freedom = n - 1

= 41 - 1

= 40

Here at df 40 & 0.01 significance level t value is 2.76

Here we reject the Ho null hypothesis due to that t > 2.76

So by observing we conclude that there is a sufficient evidence to conclude that there is significant improvement in children’s reading skills.

b)

Now to give cohen’s d

Cohen’s d = t/sqrt(n)

substitute the known values

= 3.4648/sqrt(41)

= 0.5411

c)

Here the conclusions demonstrating that there was a significant improvement in chidren's reading skills

MD= 4.9,

Standard deviation = 9.06

t(40) = 3.46,

p < .01,

d=0.54.