Question

In explaining why their country is an attractive place to invest, the Minister of Commerce from Turgistan has argued that the political problems have been exaggerated and that fewer people have been imprisoned for political reasons than you have been led to believe. However, Amnesty International reports that one third of the prisoners in Turgistan are political prisoners. A representative from your company visited a prison and sampled 500 prisoners in Turgistan, concluding that 90 of them are political prisoners. Test the hypothesis, at the 5% significance level, that one third of the prisoners in Turgistan are political prisoners.

Required:
a. Does this data support the Minister of Commerce or Amnesty International?
b. What other issues might be important when evaluating this data?

Answer 1

Answer:

a

   This data does not  support the Minister of Commerce or Amnesty

International

b

Another issue that is  important when evaluating this data is the judicial system of the Turgistan

Step-by-step explanation:

From the question we are told that

  The  sample size is  n  =  500

 The  number of political  prisoners is  k  =  90

  The  level of significance is  $\alpha = 0.05$

 

        The null hypothesis  is  $H_o  :  p =  \frac{1}{3} =  0.33$

        The alternative hypothesis is  $H_a : p \ne  0.33$

Generally the sample proportion is mathematically represented as

      $\^ p  =  \frac{k}{n}$

=>   $\^ p  =  \frac{90}{500}$

=>   $\^ p  =  0.18$

 Generally the test statistics is mathematically represented as

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

=>  $z =  \frac{0.18  -  0.40}{\sqrt{\frac{0.33 (1- 0.33)}{500} } }$      

=>  $z = -7.1429$

Generally the p-value is mathematically represented as

      $p-value  =  2 *  P( Z  >  -7.1429)$

From the normally distribution table

    The  probability of $P( Z  >  -7.1429)  =  0$

=>     $p-value  =  2 * 0$

=>     $p-value  =  0$  

From the value obtained we see that the $p-value  <  \alpha$ hence the decision rule is

  Reject the null hypothesis

The conclusion is  

  There is no sufficient evidence to conclude that  this data does support the Minister of Commerce or Amnesty International

jj