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Do the survey data provide sufficient evidence to back up the president’s claim? Carry out an appropriate hypothesis test at the 1% significance level.
 
(i) (1 mark) Identify the population of interest.
 
(ii) (2 marks) State the null and the alternative hypotheses. Define all your notation.
 
(iii) (2 marks) State the Type I and Type II errors in the context of this question.
 
(iv) (1.5 marks) List and check any required assumptions/conditions to conduct the hypothesis test in the context of the question.
 
(v) (2 marks) Compute the test statistic.
 
(vi) (2 marks) Obtain the P-value. Clearly explain your steps. Provide a sketch of your model, shade and label the relevant areas.
 
(vii) (1 mark) State your conclusion in the context of the question.
 
(viii) (0.5 mark) Based on your conclusion in the previous part, what error are you in a position of committing?