Question

Research shows that many banks are unwittingly training their online customers to take risks with their passwords and other sensitive account information, leaving them more vulnerable to fraud (Yahoo, July 23, 2008). Even web-savvy surfers could find themselves the victims of identity theft because they have been conditioned to ignore potential signs about whether the banking site they are visiting is real or a bogus site served up by hackers. Researchers at the University of Michigan found design flaws in 78% of the 214 U.S. financial institution websites they studied.
Required:
Is the sample evidence sufficient to conclude that more than three out of four financial institutions that offer online banking facilities are prone to fraud? Use a 5% significance level for the test.

Answer 1

Answer:

Decision rule

Fail to reject the null  hypothesis

Conclusion

The sample evidence is not sufficient to conclude that more than three out of four financial institutions that offer online banking facilities are prone to fraud.

Step-by-step explanation:

From the question we are told that

  The sample size is  n =  214

   The sample proportion is p = 0.78

   The level of significance is $\alpha = 0.05$

Generally the population proportion is mathematically represented as

      $p = \frac{3}{4} =0.75$ (gotten from the statement  ''three out of four'' in the question)

The null hypothesis is $H_o : p = 0.75$

The alternative hypothesis $H_a : p > 0.75$

Generally the test statistics is mathematically represented as

     $z = \frac{\^{p} - p}{ \sqrt{\frac{p(1-p)}{n} } }$

=>    $z = \frac{0.78- 0.75}{ \sqrt{\frac{ 0.75(1-0.75)}{214} } }$

=>  $z = 1.01$

Generally the p-value is mathematically represented as

    $p-value = P(Z > z )$

=> $p-value = P(Z > 1.01 )$

From the z-table  

    $P(Z > 1.01 ) = 0.15625$

So

    $p-value = 0.15625$

From the obtained values we see that $p-value > \alpha$ hence we fail to reject the null hypothesis

 Therefore we can conclude that the sample evidence is  not  sufficient to conclude that more than three out of four financial institutions that offer online banking facilities are prone to fraud.