1. A researcher is interested in estimating the average amount of sleep obtained by first- year students at MacEwan University. The researcher obtains a random sample of 50 first-year students from MacEwan from which she obtains an average of 6.5 hours of sleep.

a) Identify each of the following (5 marks-1 mark each)

i) The population ii) The sample

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)

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 0, using the 5% significance

level, then the corresponding 95% confidence interval will contain 0. (1 mark)

c) For any positive value z, it is always true that ( > ) > ( > ), where

(0,1), and , 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 = 3.15 oz. Assume that the standard deviation of the weight of allStella'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)

c)Does the interval in part (b) give evidence that the average weight of Stella's new-born kittens differs from 3.5 oz? Explain. (3 marks)

d)In order for the above inferences to be valid, it is necessary for us to assume the sample is randomly selected from a normally distributed population. Are there any indications that either of these assumptions are violated? Explain.Hint:To check one of these assumptions, you will find it helpful to construct a histogram or a stem-and-leaf display. (4 marks).