留学生2B03讲解、辅导Statistical Inference

2B03 Assignment 3

Sampling Distributions and Statistical Inference (Chapters 5, 6 & 7)

Your Name and Student ID

Due Wednesday October 30 2018 (due in class prior to the start of the lecture)

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).

5. I wish to estimate the proportion of defectives in a large production lot with plus or minus D = 0.05

of the true proportion, with a 95% level of confidence. From past experience it is believed that the

true proportion of defectives is π = 0.03. How large a sample must be used? (Hint: Use a normal

approximation for the sample proportion Pˆ - this question is worth 2 marks).

6. A cereal company checks the weight of its breakfast cereal by randomly checking 62 of the boxes. This

particular brand is packed in 20-ounce boxes. Suppose that a particular random sample of 62 boxes

results in a mean weight of 19.98 ounces. How often will the sample mean be this low, or lower if µ = 20

and σ = 0.10 (this question is worth 4 marks)?