FAD1015: Mathematics III — Tutorial 9

Centre for Foundation Studies in Science
Universiti Malaya
Session 2024/2025

Topic: Sampling Types

Question 1

For a study that consists of personal interviews with participants (rather than mail or phone surveys), explain why simple random sampling might be less practical than some other sampling methods.

Question 2

A population has four members (called A, B, C, D). You would like to select a random sample of n=2 which you decide to do in the following way: Flip a coin; if its heads, the sample will be items A and B. If its tails, the sample will be items C and D. Although this is a random sample, it is not a simple random sample. Explain why.

Question 3

Suppose that 5000 invoices are separated into four years: 2018, 2019, 2020 and 2021, each contains 50, 500, 1000, and 3450 invoices respectively. A sample of 500 sales invoices is needed.

(a) What type of sampling should you do?

(b) Explain how you would carry out the sampling according to the method stated in (a).

(c) Why is the sampling in (a) not simple random sampling?

Question 4

What is the difference between a population distribution and a sampling distribution?

Topic: Sampling Distributions

Question 5

Given a normal distribution with $\mu = 50$ and $\sigma = 5$, if you select a sample of n=100 randomly, what is the probability that the sample mean is:

(a) Less than 47?

(b) Between 47 and 49.5?

(c) Above 51.1?

Question 6

The following data represent the number of days absent per year in a population of six employees of a small company:

$$1 \quad 3 \quad 6 \quad 7 \quad 9 \quad 10$$

(a) Assuming that you sample without replacement, select all possible samples of n=2 and construct the sampling distribution of the mean. Compute the mean of all the sample means and also compute the population mean. Are they equal? (This demonstrates the unbiased property of the sample mean).

(b) Repeat (a) for all possible sample of n=3.

(c) Compare the shape of the sampling distribution of the mean in (a) and (b). Which sampling has less variability? Why?

Question 7

The US Census Bureau announced that the median sales price of new houses sold in 2009 was $221,600 and the mean sales price was $274,300. Assume that the standard deviation of the prices is $90,000.

(a) If you select sample of n=100, what is the probability that the sample mean will be less than $300,000?

(b) If you select sample of n=100, what is the probability that the sample mean will be between $275,000 and $290,000?

Related Concepts

  • Simple Random Sampling — every member has equal chance of selection
  • Stratified Sampling — dividing population into subgroups
  • Sampling Distribution — distribution of a statistic across samples
  • Central Limit Theorem — sampling distribution approaches normal as n increases
  • Standard Error — standard deviation of the sampling distribution
  • Unbiased Estimator — expected value equals population parameter
  • Population Distribution — distribution of values in the entire population

Source: FAD1015 25-26 Tutorial 9 Questions.pdf