Question

PLEASE SHOW ALL WORKS ! STEP BY STEP ! NO SPSS THANKS

1. It is known that the scores on a standardized reading test are normally distributed with μ= 75 and σ=25. A researcher suspects that special training in reading skills will produce a change in the scores for the individuals in the population. A sample of n=25 individuals is selected, and the treatment is given to this sample. Following treatment, the average score for this sample is M=80. Is this enough evidence to conclude that the training has an effect on the test scores? Use α = 0.05 (7pts)
   1. State the hypotheses.
   2. What is the percentage of the risk that we will commit a Type 1 error?
   3. Locate the critical region
   4. Compute the test statistic.
   5. Make a decision about the null hypothesis.
   6. Write a sentence discussing your conclusion. Be sure to relate it back to the information provided in the question.
   7. Identify Cohen’s d value and discuss the effect size.

Answer 1

a. Here claim is that mean is changed from 75

So hypothesis is vs

b. Here α = 0.05, so percentage of the risk that we will commit a Type 1 error is 5%

c. The z-critical values for a two-tailed test, for a significance level of α=0.05

zc​=−1.96 and zc​=1.96

Graphically

d. Test statistics is

e. As test statistics do not fall in the reject region we fail to reject the null hypothesis

f. Hence we do not have sufficient evidence to support that mean is changed from 75.