Chapter PVI, Problem 22RE

To determine

To explain is there evidence of lower scores with uncertified teachers.

Answer to Problem 22RE

There is insufficient evidence of lower scores with uncertified teachers.

Explanation of Solution

It is given in the question that several programs attempt to address the shortage of qualified teachers by placing uncertified teachers in school with acute needs often in inner cities. Thus, for testing the hypothesis we will use the calculator $\text{TI}-89$ as, first we will go in the STAT TESTS menu, choose $4:2-$ SampTTest. Then you must specify if you are using data stored in two lists or if you will enter the means, standard deviations, and sizes of both samples. You must also indicate whether to pool the variances (when in doubt, say no) and specify whether the test is to be two-tail, lower-tail, or upper-tail. So, now we will define the hypothesis as:

  $\begin{array}{l}{H}_0:{\mu }_1={\mu }_2\\ H_a:{\mu }_1>{\mu }_2\end{array}$

And also given,

  $\begin{array}{l}{n}_1=44\\ {\overline{x}}_1=35.62\\ s_1=9.31\\ n_2=44\\ {\overline{x}}_2=32.48\\ s_2=9.43\end{array}$

Thus, by using the calculator $\text{TI}-89$ , the test statistics and the P-value is as:

  $\begin{array}{l}P=0.0599\\ t=1.57\end{array}$

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

  $P>0.05\Rightarrow \text{Fail to Reject }{H}_0$

Thus, we conclude thatthere is insufficient evidence of lower scores with uncertified teachers.