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Sampling Distributions and Statistical Inference
Instructions: You are to use R Markdown for generating your assignment (see the item Assignments
and R Markdown on the course website for helpful tips and pointers).
1. Define the following terms in a sentence (or short paragraph) and state a formula if appropriate (this
question is worth 5 marks).
i. Estimator
ii. Interval Estimate
iii. Efficiency
iv. Consistency
v. Hypothesis Test
2. If the income in a community is normally distributed, with a mean of $39,000 and a standard deviation
of $8,000, what minimum income does a member of the community have to earn in order to be in the
top 5%? What is the minimum income one can have and still be in the middle 50% (this question is
worth 4 marks)?
3. Suppose that the number of hours per week of lost work due to illness in a certain automobile assembly
plant is approximately normally distributed, with a mean of 45 hours and a standard deviation of 15
hours. For a given week, selected at random, what is the probability that (this question is worth 3
marks):
i. The number of lost work hours will exceed 70 hours?
ii. The number of lost work hours will be between 30 and 45 hours?
iii. The number of lost work hours will be exactly 50 hours?
4. A senator claims that 60% of her constituents favour her voting policies over the past year. In a random
sample of 50 of these people, the sample proportion of those favoured her voting policies was only 0.4. Is
this enough evidence to make the senator’s claims strongly suspect? (Hint: Use a normal approximation
to the binomial distribution then construct a confidence interval - this question is worth 2 marks).