Chapter 9.2, Problem 52E

To determine

To find: Whether the proportion of students who think that well-off is different from the national value of 73% or not.

Explanation of Solution

Given:

  $\begin{array}{l}\text{Hypothesized proportion}\left(p_o\right)=73\%=0.73\\ \text{Sample proportion}\left(\widehat{p}\right)=\frac{132}{200}=0.66\\ \text{Level of significance}\left(\alpha \right)=0.05\end{array}$

Formula used:

The formula to compute the test statistic is:

  $z=\frac{\widehat{p}-p_0}{\sqrt{\frac{p_0\left(1-p_0\right)}{n}}}$

Calculation:

The null and alternative hypotheses are written as:

  $\begin{array}{l}{H}_0:p_0=0.73\\ H_a:p_0\ne 0.73\end{array}$

The obtained Minitab output is:

  

Here, p -value is less than the level of significance. The null hypothesis is rejected.

Conclusion:

At 5% level of significance there are sufficient evidence to conclude that the proportion of students who think that well-off is different from the national value of 73%.