Question 1 (15 marks)

• From a random sample of 500 Montrealers, 400 indicated that they were in favour of the proposed policy to ban single-use plastic bags on the island. Test at the 10% significance level a politician's statement that "those who are in favour of this policy represent more than 85% of the population."

Formulate the null and alternative hypotheses. [2 marks]

State the decision rule for this test. [2 marks]

Calculate the appropriate statistic for testing the null hypothesis. [2 marks]

Should the null hypothesis be rejected or not rejected? [1 mark]

What is your conclusion regarding the politicians statement? [3 marks]

• Suppose that the true proportion of those who favour this policy is 0.77. Calculate the power of the test conducted in (a). [5 marks]