1. You are asked to conduct the following one-sided hypothesis test: Null hypothesis: The population mean wage per hour in Ontario is higher than $30. H02M>30 Alternative hypothesis: The population mean wage per hour in Ontario is equal or lower than $30. H1 : p, s 30 To conduct the hypothesis test, you collected information on hourly wages (Xi) from a sample of 49 workers in Ontario, and calculated the sample mean (X) and sample variance (s2): )2 = 25 and s2 = 36. Recall that the T-statistic is given by X u = N trail: 3/ (/13 where n 1 denotes the degree of freedom and n is the number of observations. 15 (a) What is the critical value corresponding to a signicance level 0.05? (5 points) (Hint: The onesided hypothesis test is different from the twosided test, introduced in Lecture 2. In a two~sided test, you reject the null hypothesis when the absolute value of t is too largeLe, the sample mean is either far greater or smaller than the proposed population mean (,a) Here, you reject the null only when t is too smallLe, the sample mean is far smaller than u. How does this aect your choice of the critical value for a given signicance level?) (b) Will you reject the null hypothesis and why? (5 points) 2. Based on X and 32 in part 1, calculate the interval that contains the true population mean with a 95% probability. (5 points)