Question

In explaining why their country is an attractive place to invest, the Minister of Commerce
from Desertia 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
Desertia are political prisoners. A representative from your company visited a prison and
sampled 500 prisoners in Desertia, concluding that 90 of them are political prisoners.
Test the hypothesis, at the 5% significance level, that one third of the prisoners in
Desertia are political prisoners. Does this data support the Minister of Commerce or
Amnesty International? What other issues might be important when evaluating this data?

Answer 1

Amnesty International reports that one third of the prisoners in Desertia are political prisoners is 1/3= 0.33

NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha:

alpha= 0.05

Under null hypothesis H0

p= x/n= 90/500= 0.18

Z critical for left tailed test at 0.05 level of significance is -1.645

CONCLUSION: SINCE CALCULATED VALUE OF Z IS SMALLER THAN CRITICAL VALUE OF Z FOR LEFT TAILED TEST. THEREFORE WE REJECT NULL HYPOTHESIS AT 0.05 LEVEL OF SIGNIFICANCE. This data support the Minister of Commerce.