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Asia Pacific (APAC) Fraud Survey, out of 1508 respondents surveyed in 2015, 680 said that their companies had not implemented a whistle-blower hotline

That is

The size of the sample is$n_1=1508$

The sample proportion is

$$\begin{gathered} {\hat{p}}_1=\frac{x_1}{n_1} \\ =\frac{680}{1508} \\ =0.451 \end{gathered}$$

And

Also,out of 681 respondents surveyed in 2013, 436 said that their companies had not implemented a whistle-blower hotline.

That is

The size of the sample is$n_2=681$

The sample proportion is

$$\begin{gathered} {\hat{p}}_2=\frac{x_2}{n_2} \\ =\frac{436}{681} \\ =0.640 \end{gathered}$$

We have to test

$H_0:p=.5$

Against

$H_a:p<.5$

The test statistic for testing these hypotheses is

$$\begin{gathered} Z=\frac{{\hat{p}}_1-p}{\sqrt{\frac{p\left(1-p\right)}{n_1}}} \\ =\frac{0.451-0.50}{\sqrt{\frac{0.50\left(1-0.50\right)}{1508}}} \\ =\frac{-0.049}{\sqrt{0.00016578}} \\ =-3.81 \end{gathered}$$

Now critical value at a 5% significance level using the standard normal table is

$$\begin{gathered} Z_{伪}=Z_{0.05} \\ =-1.645\left(alternativehypothesisisleft-tailed\right) \end{gathered}$$

We can see that

$Z<Z_{伪}$

Hence, we reject the null hypothesis $H_0$.

Interpretation:

At the 5% significance level, we have sufficient evidence to conclude that the true proportion of companies that had not implemented a whistle-blower hotline in 2015 is less than 50%.

We have to test

$H_0:p=.5$

Against

$H_a:p>.5$

The test statistic for testing these hypotheses is

$$\begin{gathered} Z=\frac{{\hat{p}}_2-p}{\sqrt{\frac{p\left(1-p\right)}{n_2}}} \\ =\frac{0.640-0.50}{\sqrt{\frac{0.50\left(1-0.50\right)}{681}}} \\ =\frac{0.14}{\sqrt{0.00036711}} \\ =7.31 \end{gathered}$$

Now critical value at a 5% significance level using the standard normal table is

$$\begin{gathered} Z_{伪}=Z_{0.05} \\ =1.645\left(alternativehypothesisisright-tailed\right) \end{gathered}$$

We can see that

$Z>Z_{伪}$

Hence, we reject the null hypothesis $H_0$.

Interpretation:

At the 5% significance level, we have sufficient evidence to conclude that the true proportion of companies that had not implemented a whistle-blower hotline in 2013 is greater than 50%.