Chapter PV, Problem 16RE

(a)

To determine

To write a $95\%$ confidence interval for the increase in the proportion of women who may develop side effects from this treatment and interpret your interval.

Answer to Problem 16RE

  $(0.1814,0.20777)$ .

Explanation of Solution

It is given in the question about the disease eclampsia. Therefore, now, to find the confidence interval we will use the calculator $\text{TI}-89$ . So, we have to first go to the STAT $\text{Ints}$ menu and select $6:2-\text{PropZInt}$ . Then we have to enter the observed counts and the sample sizes for both the samples. Then specify a confidence level. Then the interval will be calculated. Thus, we have,

  $\begin{array}{l}{x}_1=40\\ n_1=4999\\ x_2=96\\ n_2=4993\\ \alpha =0.05\end{array}$

Thus, the confidence interval will be as:

  $(0.1814,0.20777)$ .

Thus, we interpret from the confidence interval that we are $95\%$ confident that increase in the proportion is between $(0.1814,0.20777)$ .

(b)

To determine

To explain is there evidence that that the treatment may be effective in preventing the development of eclampsia and test an appropriate hypothesis and state your conclusion.

Answer to Problem 16RE

There is evidence that the treatments of Magnesium sulfate decreased the occurrence of Eclampsia for people at risk of Eclampsia.

Explanation of Solution

It is given in the question about the disease eclampsia. Thus, the confidence interval will be as:

  $(0.1814,0.20777)$ .

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,

  $\begin{array}{l}{x}_1=40\\ n_1=4999\\ x_2=96\\ n_2=4993\\ \alpha =0.05\\ H_0:p_1=p_2\\ H_a:p_1<p_2\end{array}$

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,

  $P=0.000000643$

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 conclude that there is evidence that the treatments of Magnesium sulfate decreased the occurrence of Eclampsia for people at risk of Eclampsia.