Chapter 9.2, Problem 42E

To determine

To find: Whether there is sufficient evidence to conclude that the claim of manufacturer is true at 5% significance level.

Answer to Problem 42E

No, there is insufficient evidence to conclude that the claim of manufacturer is true at 5% significance level.

Explanation of Solution

Given:

Population proportion ( p ) = 37%

Number of patients ( n ) = 300

Number of patients that experienced nausea ( x ) = 25

Formula used:

The formula to compute the test statistic is:

  $\begin{array}{l}z=\frac{\widehat{p}-p_0}{\sqrt{\frac{p_0\left(1-p_0\right)}{n}}}\\ \text{Where,}\\ \widehat{p}=\frac{x}{n}\end{array}$

Calculation:

The null and alternative hypotheses are:

  $\begin{array}{l}{H}_0:p=0.10\\ H_a:p<0.10\end{array}$

The obtained output using Ti-83 plus calculator is:

  

Conclusion:

From the above obtained output, the p -value is 0.1680 which is above significance level of 0.05. The null hypothesis is not rejected. Thus, there are insufficient evidence to agree with the claim of manufacturer at 5% significance level.