Chapter PV, Problem 21RE

(a)

To determine

To test an appropriate hypothesis and state your conclusion.

Answer to Problem 21RE

There is no evidence to show that the accident rate is lower for teenagers girls.

Explanation of Solution

It is given in the question that traffic are the leading cause of death among people. The assumptions and conditions for the inferences are as:

Random condition: It is satisfied as the insurance company is randomly selected.

Independence condition: It is satisfied as groups are independent.

Success/failure condition: It is satisfied as,

  $\begin{array}{l}np=44>10\\ n(1-p)=344>10\end{array}$

  $\begin{array}{l}np=55>10\\ n(1-p)=333>10\end{array}$

Therefore, all the conditions are met. Thus, to calculate an appropriate hypothesis we will use $\text{TI}-89$ calculator. Thus, for this first we have to select $6:2-\text{PropZInt}$ from the STAT TESTS menu. Then, enter the observed counts and sample sizes for both the samples. 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,

  $\begin{array}{l}{x}_1=44\\ n_1=388\\ x_2=55\\ n_2=388\\ \alpha =0.05\\ H_0:p_1=p_2\\ H_a:p_1<p_2\end{array}$

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,

  $P=0.1183$

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

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

Thus, we conclude that there is no evidence to show that the accident rate is lower for teenagers girls.

(b)

To determine

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

Explanation of Solution

It is given in the question that traffic are the leading cause of death among people. The value of z-statistics and the P-value will be then,

  $P=0.1183$

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

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

Thus, we conclude that there is no evidence to show that the accident rate is lower for teenagers girls. Thus, if the null hypothesis is true this result will occur $11.83\%$ of the time.