Chapter PV, Problem 6RE

(a)

To determine

To find out what kind of study is this.

Answer to Problem 6RE

It is an experiment.

Explanation of Solution

It is given in the question that a British physician who was interested in the role of bacteria in human infections. So, he conducted the experiment for the same. Thus, it is also given that,

  $\begin{array}{l}{x}_1=34\\ n_1=40\\ x_2=19\\ n_2=35\\ \alpha =0.05\end{array}$

So, as we know an experiment deliberately imposes some treatment on individuals in order to observe their responses. And an observation study tries to gather information without disturbing the scene they are observing. Thus, this study is an experiment because the treatment were assigned to the patients with carbolic acid and no carbolic acid.

(b)

To determine

To explain what do you conclude and support your conclusion by testing an appropriate hypothesis.

Answer to Problem 6RE

There is sufficient evidence to support the claim that carbolic acid is effective in increasing the chances of surviving an assumption.

Explanation of Solution

It is given in the question that a British physician who was interested in the role of bacteria in human infections. So, he conducted the experiment for the same. 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,

  $\begin{array}{l}{x}_1=34\\ n_1=40\\ x_2=19\\ n_2=35\\ \alpha =0.05\\ H_0:p_1=p_2\\ H_a:p_1>p_2\\ \alpha =0.05\end{array}$

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,

  $\begin{array}{l}P=0.0018\\ z=2.91\end{array}$

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 conclude that there is sufficient evidence to support the claim that carbolic acid is effective in increasing the chances of surviving an assumption.

(c)

To determine

To explain what reservation do you have about the design of the study.

Explanation of Solution

It is given in the question that a British physician who was interested in the role of bacteria in human infections. So, he conducted the experiment for the same. As we are unaware if the patients were randomly assigned to a treatment and we are also unaware if the patients were aware of which treatment they received. If these two conditions are not satisfied then it is likely that the results of the experiment are biased.