Question

A teacher gives a reading skills test to a third-grade class of n = 25 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 MD = 5.7 points with s2 = 100. A. Are the results sufficient to conclude that there is a significant improvement in children’s reading skills? Use a one-tailed test with α = .01. B. Compute estimated Cohen’s d to measure the size of the effect. Is this a large effect? C. Write a conclusion demonstrating how the outcome of the hypothesis test would appear in a research report in APA style.

Answer 1

Answer:

Given,

xbar = 5.7

sample size = n = 25

standard deviation = s^2 = 100

s = 10

Null hypothesis

Ho : mu = 0

Alternative hypothesis

Ha : mu > 0

Confidence interval = 99%

significance level = 0.01

Now,

degree of freedom = n - 1

= 25 - 1

df = 24

Now to give the test statistic

Z = (x - mu) / (s/sqrt(n))

substitute the known values in above formula

Z = (5.7 - 0)/(10/sqrt(25))

= 5.7/2

Z = 2.85

At the 99% confidence interval, degree of freedom = 24 ,

Z value is 2.80

i.e.,

z > 2.80

Here we observed that, Z > z i.e., 2.85 > 2.80 . so reject the null hypothesis Ho

So we can say that the students are not improved at 99% confidence interval i.e., 0.01 significance level.