Chapter 9, Problem 6CRE

a.

To determine

To check: Whether the sufficient evidences are provided the data that there has been decrease in blood pressure of the individual during this year at 5% significance level.

Answer to Problem 6CRE

Yes, there is sufficient evidence.

Explanation of Solution

Given:

  $\begin{array}{l}\text{Population mean}\left(\mu \right)=0\\ \text{Sample mean}\left(\overline{x}\right)=-6\\ \text{Sample size}\left(n\right)=50\\ \text{Sample standard deviation}\left(s\right)=19.8\end{array}$

Formula used:

The formula to compute the test statistic is:

  $t=\frac{\overline{x}-\mu }{\frac{s}{\sqrt{n}}}$

Calculation:

Using the information, the null and alternative hypotheses are:

  $\begin{array}{l}{H}_0:\mu =0\\ H_a:\mu <0\end{array}$

Using the Ti-83 calculator the output is:

  

Decision rule:

The p-value is less than the significance level. Thus, decision is written as the rejection of the null hypothesis.

Conclusion:

At 5% significance level, there are sufficient evidence to support the provided claim.

b.

To determine

To find: Whether health campaign has reduced the blood pressure.

Answer to Problem 6CRE

No.

Explanation of Solution

Since, the observational study does not influence the outcome and the provided case is an observational study. Thus, conclusion cannot be drawn here.