2B03 Assignment 3
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2B03 Assignment 3∗
Sampling Distributions and Statistical Inference (Chapters 5, 6 & 7)
Instructions: You are to use Quarto Markdown for generating your assignment output file. You begin with the Quarto Markdown script downloaded from A2L, and need to pay attention to information provided via introductory material posted to A2L on working with R and Quarto Markdown. Having added your answers to the Quarto Markdown script, you then are to generate your output file using the “Render” button in the RStudio IDE and, when complete, upload both your Quarto Markdown file and your PDF file to the appropriate folder on A2L.
1. Define the following terms in a sentence (or short paragraph) and state a formula if appropriate (this question is worth 5 marks).
a. Hypothesis Test
b. Estimator
c. Interval Estimate
d. Efficiency
e. Consistency
2. If the income in a community is normally distributed, with a mean of $28,000 and a standard deviation of $5,000, what maximum income does a member of the community have to earn in order to be in the bottom 20%? What is the maximum 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 12 hours. For a given week, selected at random, what is the probability that (this question is worth 3 marks):
a. The number of lost work hours will exceed 70 hours?
b. The number of lost work hours will be between 30 and 40 hours?
c. 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 40 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 = 0.02 of the true proportion, with a 95% level of confidence. From past experience it is believed that the true proportion of defectives is π = 0.02. How large a sample must be used? (Hint: Use a normal approximation for the sample proportion P - 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 20.04 ounces. How often will the sample mean be this high, or higher if μ = 20 and σ = 0.10 (this question is worth 4 marks)?
2023-10-30
Sampling Distributions and Statistical Inference