# 2B03 Assignment 3

## R Language Assignment Question

2B03 Assignment 3

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 Assignment website for helpful tips and pointers).

- >Define the following terms in a sentence (or short paragraph) and state a formula if appropriate (this question is worth 5 marks).
- Sampling Distribution
- Estimate
- Interval Estimate
- Bias
- Hypothesis Test
- 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):
- The number of lost work hours will exceed 75 hours?
- The number of lost work hours will be between 35 and 45 hours?
- The number of lost work hours will be exactly 45 hours?
- 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)?
- 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 0.5. Is this enough evidence to make the senatorâ€™s claims strongly suspect? (Hint: Use a normal approximation to the binomial distribution then construct a confidence interval â€“ this question is worth 2 marks).
- 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 20.02 ounces. How often will the sample mean be this high, or higher if Î¼ = 20 and Ïƒ = 0.10 (this question is worth 4 marks)?
- 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 90% level of confidence. From past experience it is believed that the true proportion of defectives is Ï€ = 0.02. How large a sample must be used? (Hint: Use a normal approximation for the sample proportion PË† â€“ this question is worth 2 marks).

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