Statistics Canada indicates that one in four {25%) Canadians aged 18 and older screened positive for symptoms of depression, anxiety or posttraumatic stress disorder {PTSD} in Spring 2021, There has been ongoing concern that the pandemic has aected the mental health of Canadians, particularly those who have experienced impacts of the pandemic such as social isolation, job loss, or changes in relationships Assuming the rate of depression, anxiety or posttraumatic stress disorder was same for the University of Ottawa students in 2022 winter, you tool: a random sample of 200 students, where 75 were screened positive for the symptoms, Do you think the mental well-being of the University of Ottawa students is worse than that of Canadian population reported by Statistics Canada in 2022 winter? (a) [10] Test at 5% level of signicance whether the proportion of University of Ottawa students having positive symptoms of depression, anxiety or posttraumatic stress disor- der {PTSD} is higher than that of Canadian population reported by Statistics Canada. Use both critical value and pvalue approach showing detailed manual calculation of the steps of hypotheses (hypotheses, decision zone, critical value, pvalue, decision with justication). (Manual Calculation) (b) [T] For testing the same hypotheses, calculate manually an appropriate 95% condence interval for the proportion of University of Ottawa students having positive symptoms of depression, anxiety or posttraumatic stress disorder (PTSD) higher than 25% (i.e., national rate). Interpret the condence interval. Does this interval allow you to make the same conclusion as in part (a)? Explain (Manual Calculation] (c) [3] How large sample size would you need to estimate, within 4%, of the true pro- portion with 98% condence? Assume there is no prior knowledge of 36 (Manual Calculation] (d) [5] Perform the hypothesis tests of (a) and (b) using MINITAB and include your output in the assignment. Do you have the same result as manual calculation? Verify. (NHNITAB)