In comparing the performance of first-grade students in his district with the national norm of 100 on a widely used IQ test, the results for a random sample of his first graders lead him to retain Ho: ? = 100 (? = .01) for his population. He concludes, 'My research proves that the average first grader in our district falls right on the national norm of 100'. Any comment? Compare what we learn when we reject Ho with what we learn when we retain Ho.
Let us think of hypothesis testing like a judicial trial. In a judicial trial, a defendant is presumed innocent unless proven guilty. Thus, the null hypothesis is that the defendant is innocent. The alternative hypothesis is that the defendant is guilty. When there is enough evidence to conclude that the defendant is guilty (i.e., the defendant is convicted), the null hypothesis of innocence is rejected in favor of the alternative hypothesis. When there is not enough evidence for the jury to conclude that the defendant is guilty (i.e., the ...
The performance of first grade students versus the national normal is examined in the solution.