Mental measurements of young children are often made by giving them blocks and telling them to build a tower as tall as possible. One experiment of block building was repeated a month later, with the times (in seconds) listed in the accompanying table (based on data from "Tower Building" by Johnson and Courtney, Child Development, Vol. 3). The previous experiment shows that the times are normally distributed. Use a 0.01 level of significance to test the claim that there is no difference between the two times.
Child First Trial: 30 19 19 23 29 178 42 20 12 39 14 81 17 31 52
Second Trial: 30 14 8 14 52 14 22 17 8 11 30 14 17 15
Solve first for the mean and standard deviation: Use the standard deviation formula with n-1 as the denominator.
a. Claim (in symbolic form): Ho: μ1 = μ2
Ha: μ1 ≠μ2
b. Level of significance: 0.01
Decision Rule: Reject Ho if the test-statistic is greater than the critical value.
c. Test-statistic: Calculate the t-statistic using the formula:
t = (x̄1 - x̄2) / √((s1^2 / n1) + (s2^2 / n2))
d. Computation: Calculate the mean and standard deviation for each trial, then calculate the test-statistic.
e. Decision: Compare the test-statistic to the critical value.
f. Conclusion: Based on the test results, either reject Ho or fail to reject Ho.