4. An economist would recommend that the Bank of Canada change the interest rate for borrowed...

4. An economist would recommend that the Bank of Canada change the interest rate for borrowed money if the average annual inflation rate is less than 2.15%. Based on a sample from the past 21 years, the average annual inflation rate was 1.87%, with a standard deviation of 0.67%. Assume the population is approximately normally distributed.

(a) [1 mark] Define the parameter you are testing.

(b) [1 mark] State the null hypothesis and alternative hypothesis you would use to test whether there was sufficient evidence that the average annual inflation rate was less than 2.15%.

(c) [1 mark] Assuming that H0 is true, what is the formula for the appropriate test statistic? How is it distributed? If it is t-distributed, be sure to indicate the number of degrees of freedom.

(d) [1 mark] Compute the observed value of the test statistic.

(e) [2 marks] Determine the p-value to within table accuracy. If your test statistic is zdistributed, this will be an exact value; if your test statistic is t-distributed, indicate the tightest possible bounds on the p-value.

(f) [1 mark] Report the strength of the evidence against H0 in favour of H1.

(g) [1 mark] Report the estimated value of the parameter and the estimated standard error.

(h) [2 marks] Would you reject your null hypothesis H0 when using a significance level of α = 0.01? Write a concluding sentence about the economist’s decision regarding the mean annual inflation rate.

Expert Solution

orchestra answered 1 year ago

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