Chapter 21, Problem 8E

(a)

To determine

To explain what the P-value means in this context.

Explanation of Solution

It is given in the question that a new reading program may reduce the number of elementary school students who read below grade level. Statistical analysis of the results showed that the percentage of students who did not meet the grade-level goal was reduced from $15.9\%\text{ to 15}\text{.1\%}$ . The hypothesis that the new reading program produced no improvement was rejected with a P-value of $0.023$ . Thus, the P-value means in this context that there is a $2.3\%$ chance of seeing a sample proportion of $15.1\%$ of students not attaining a grade level by natural sampling variation alone if $15.9\%$ is the true population value.

(b)

To determine

To explain why you not recommend that your local school adopt it.

Answer to Problem 8E

Explanation of Solution

It is given in the question that a new reading program may reduce the number of elementary school students who read below grade level. Statistical analysis of the results showed that the percentage of students who did not meet the grade-level goal was reduced from $15.9\%\text{ to 15}\text{.1\%}$ . The hypothesis that the new reading program produced no improvement was rejected with a P-value of $0.023$ . Thus, we would not recommend that your local school adopt it because with the older methods, $1352$ students would not be expected to read at grade level, but with the new program, $1284$ would be expected to not read at grade level. This decrease and the significance of this decrease would depend on the costs of switching to the new program.