Economics 2122A Econometrics I Assignment 5

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Question 1 (Show your steps, not only the final result)

A random sample of 12 employees in a large manufacturing plant found the following figures for number of hours of overtime worked in the last month:

22 16 28 12 18 36 23 11 41 29 26 31

Propose an unbiased point estimator for the population proportion of employees working more than 30 hours of overtime in this plant in the last month and compute the corresponding estimate.

Question 2 (Show your steps, not only the final result)

Consider the example, where company A is sending a shipment to company B. Company A claims that at most 2% of its products is defective. Company B decides to test this claim by collecting a random sample of 900 products and accept the shipment unless it is significantly evident that the defective proportion is higher than 2%. Suppose 20 out of these 900 products are defective, how would you determine whether company B should accept the shipment or not under 5% significance level? Perform a hypothesis test to answer.

Question 3 (Show your steps, not only the final result)

A company produces electric devices operated by a thermostatic control. The variance of the operating temperature (which is normally distributed) should not exceed 4°F. For a random sample of 20, the sample standard deviation of operating temperatures was 2.36°F. According to this sample, is it significantly evident that the operating temperature standard (e.g., variance not exceeding 4°F) is met at the 5% significance level? Perform a hypothesis test to answer.

Question 4 (Show your steps, not only the final results.)

Consider the relationship between prices and quantity supply of some product, modelled as follow Bo+ Bprice+U,

How would you interpret B₀ and B₁ economically?

Provide one example of the factors captured by the error term.

Question 5 (Continue to build your formula sheet)

List the important formulas/notes you would like to include in your formula sheet.

Solution – Economics 2122A Econometrics I Assignment 5

A random sample of 12 employees in a large manufacturing plant found the following figures for number of hours of overtime worked in the last month:

22 16 28 12 18 36 23 11 41 29 26 31

Propose an unbiased point estimator for the population proportion of employees working more than 30 hours of overtime in this plant in the last month and compute the corresponding estimate.

Question 1 Correct Answer:

Let’s denote the population proportion of employees working more than 30 hours of overtime in this plant in the last month as p.

We want to find an unbiased point estimator for p.

We can use the sample proportion, p̂, as an unbiased point estimator for p.

p̂ = (number of employees working more than 30 hours of overtime in the sample)/(total number of employees in the sample)

The sample mean can be an unbiased point estimator, which in this case is the sample proportion # 𝑜𝑓>30/𝑛 with 𝑛 being the sample size.

The corresponding estimate is 3/12 = 1/4.

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