Chapter 20, Problem 27E

To determine

To explain is this evidence that their dropout rate may be increasing.

Answer to Problem 27E

We have evidence that the dropout rate is increasing.

Explanation of Solution

It is given in the question that some people are concerned that new tougher standards and high stakes tests adopted in many states have driven up the high school dropout rate. Thus, the null hypothesis states that the rate is equal to $10.3\%$ . And the alternative hypothesis states that the rate is morethan $10.3\%$ . So, we define hypothesis as:

  $\begin{array}{l}{H}_0:p=0.103\\ H_a:p>0.103\end{array}$

Thus, let us check the appropriate conditions and assumptions for inference to proceed further to test hypothesis as:

Random condition: It is satisfied as we assumed that the sample was randomly selected from the population.

Independent condition: It is satisfied as we can assume that the sample is independent.

  $10\%$ condition: It is satisfied as the sample is less than $10\%$ of all population.

Success/failure condition: It is satisfied because both are greater than ten as,

  $\begin{array}{l}np=0.103(1782)>10\\ n(1-p)=0.897(1782)>10\end{array}$

Thus, all the conditions are satisfied. Thus, for this first we have to select $5:1-\text{PropZInt}$ from the STAT TESTS menu. Then, enter the observed count and sample size for the sample. Then we will indicate what kind of test we want: one-tail lower tail, two-tail, or one-tail upper tail. Then, we will specify whether to calculate the result or draw the result. Hence we have,

  $\begin{array}{l}x=210\\ n=1782\\ c=0.95=95\%\end{array}$

So, by putting the values above by using the calculator we will get the result as,

The value of z-statistics and the P-value will be then,

  $\begin{array}{l}z=2.062\\ P-\text{value}=0.020\end{array}$

And as we know if the P-value is smaller than the significance level, then reject the null hypothesis, so, we have,

  $P<0.05\Rightarrow \text{ Reject }{H}_0$

Thus, we can conclude that we have evidence that the dropout rate is increasing.