Question

22 seventh-graders were randomly selected from a middle school and their IQ was tested. One year later after they finished eighth-grade their IQ was tested again. They determined that the mean of the differences of these students was -.0121 and their standard deviation was .5. Let alpha be equal to .05. Is there enogh evidence to say that the differences between the IQs of the two academic years was less than -.01? What are the hypotheses equal to? What is the test statistic and p value?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = -0.01
Alternative Hypothesis, Ha: μ < -0.01

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (-0.0121 - -0.01)/(0.05/sqrt(22))
t = -0.197

P-value Approach
P-value = 0.4229
As P-value >= 0.05, fail to reject null hypothesis.