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.”
(i) Formulate the null and alternative hypotheses.
(ii) State the decision rule for this test.?
iii) Calculate the appropriate statistic for testing the null hypothesis.?
(iv) Should the null hypothesis be rejected or not rejected??
(v) What is your conclusion regarding the politician?s statement?
b) Suppose that the true proportion of those who favour this policy is 0.77. Calculate the power of the test conducted in (a).?
H0 : p = 0.85
Ha : p> 0.85
Zcritical = Z0.1 = 1.28
If Z > Zcritical, reject the null hypothesis
p^ = 400/500 = 0.8
Z = (p^-p)/(p * (1-p)/n) = (0.8-0.85)/sqrt(0.85 *…