Question

A teacher gives a third-grade class of n = 16 a reading skills test 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 revealed an average improvement of M_D= 4.7 points, and the variance for the difference scores is scores is s²_D = 64. Can you conclude that there is significant improvement? Use a one-tailed test with α = 0.05.

(1)What type of statistical test is appropriate for this research question?

(2) State the null and alternative hypotheses using statistical notation OR using plain English (a sentence for each)

(3) What are the degrees of freedom and critical t-value for this test?

(4) Compute the test statistic

(5) What is your decision? And what does that decision mean, or how would you interpret/explain your decision?

Answer 1

1)
paired t-test

2)
Below are the null and alternative Hypothesis,
Null Hypothesis: μ(d) = 0
Alternative Hypothesis: μ(d) > 0

3)
Rejection Region
This is right tailed test, for α = 0.05 and df = 15
Critical value of t is 1.753.
Hence reject H0 if t > 1.753

4)
Test statistic,
t = (dbar - 0)/(s(d)/sqrt(n))
t = (4.7 - 0)/(8/sqrt(16))
t = 2.35

5)
reject the null hypothesis.
There is significant improvement