iii) The population parameter iv ) The estimator of the population parameter v) The point estimate value b) Suppose the researcher obtains a 95% confidence interval of (6.1, 6.9). What is the margin of error? (2 marks) c) It is recommended that young adults sleep at least 7 hours per night . Does the interval from (b ) provide evidence that, on average, first-year students at MacEwan are under sleeping? Explain (2 marks) d) Is it necessary for the population of interest to be normally distributed for the interval in (b ) to be valid? Explain. (2 marks) e) Briefly explain why the interval estimate from (b ) is superior to the point estimate from (a). (2 marks) 2. Explain why each of the following statements is false. a) A 95% confidence interval is always wider than a 99% confidence interval (provided the intervals are constructed using the exact same data). (1 mark) b ) If a two - sided test finds sufficient evidence that H u , using the 5% significance level, then the corresponding 95% confidence interval will contain H . (1 mark) c) For any positive value z, it is always true that P (Z>z )> P (T> z ) , where Z ~ N (0,1 ), 1 T ~T , for some finite df value. (1 mark) d) If you have just constructed a 90% confidence interval, then there is a 90% chance that the interval contains the true value of the parameter of interest. (2 marks) 3. The average weight of new-born kittens is 3.5 ounces. A breeder suspects one of her cats, Stella, produces extra small kittens. The breeder's suspicions arise from the weights of Stella's most recent litter of kittens: (3.1, 3.3, 3.0, 3.7, 2.9, 2.9 ]. Note that the sample mean is * =6 3.15 oz. Assume that the standard deviation of the weight of all Stella's new-born kittens is 0.3 oz. a) Test at the 5% significance level whether the average weight of Stella's new-born kittens is below 3.5 oz. Complete all 6 steps of your hypothesis test, including a discussion of the assumptions. (8 marks) b) Obtain and interpret a 90% two-sided confidence interval for the mean weight of all Stella's new-born kittens (6 marks)