A paired-difference experiment dealing with the response latencies for noise detection under two conditions used a sample of twelve 9-month-old children and reported a sample mean difference of 70.1 and standard deviation of 49.4 for the differences (J. Morgan and J. Saffran, Child Development, Vol. 66, pp. 911-936, 1995). In their discussion, the authors reported a p-value of less than 0.01 for a two-sided alternative. Assuming that the test uses 5% signicance level,
a. Find the t-statistic.
b. Find the CI (confidence interval) associated with the test.
c. Give an interpretation of the CI in part (b).
d. Does the CI support the conclusion of the hypothesis test as reported by its p-value? What can you say about the conclusion from hypothesis tests and CI for population means in general? Explain.