Question

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.

Answer 1