Question

A survey of 1138 CEOs finds that 713 believe the economy will improve next year. We are trying to investigate if the proportion of CEOs who believe the economy will improve next year is larger than the 55%. What is the value of the test statistic Z for this test?

Answer 1

The null and alternative hypothes is is,

\(H_{0}: P=0.58\)

\( H_{1} : p>0.58\)

Given,

proporion of \(c \in 0\) beliene the economy will improve next year is,

$$ \hat{p}=\frac{x}{n}=\frac{713}{1178}=0.61 $$

The teot statistic is,

$$ \begin{aligned} z &=\frac{\hat{p}-p_{0}}{\sqrt{\frac{p_{0} a_{0}}{n}}} \\ &=\frac{0.61-0.58}{\sqrt{\frac{0.58 \times 0.42}{1178}}} \\ 2=& 2.09 \end{aligned} $$

The value of teot statistic for this teot is,

$$ z=2.09 $$