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

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STAT 151 Assignment 4 Total: 119 marks

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 contain0.(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)