Probability & Statistics for Machine Learning & Data Science (18)

Sampling and Point estimation

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Quiz

Q1

Consider the following population, P, where P = {1, 1, 3, 5, 10}

And the following sample, S, where S = {1, 3}

What is the value of the sample mean?

1. 2
2. 6
3. It cannot be computed with the given information
4. 4

Answer

1

The sample mean should be calculated from the sample set’s numbers only. Therefore, the sample mean is (1+3)/2 = 2

Q2

What is the difference between a sample and a population in statistics?

1. A sample is the entire group being studied, while a population is a subset of that group.
2. A population is the entire group being studied, while a sample is a subset of that group.
3. A population is a group from which a sample is drawn; both terms can be used interchangeably.

Answer

2

Q3

Let S be a random sample, where S = {5, 2, 7, 10}. Calculate the population variance for the sample set.

1. 2.9
2. 6
3. 8.5
4. 34

Answer

3

This was a simple application of the formula $\sigma^2 = {1\over N}\sum(x-\mu)^2$. Note that $\mu=6$. Therefore: $\sigma^2={1\over4}((5-6)^2+(2-6)^2+(7-6)^2+(10-6)^2)={1\over4}(1+16+1+16)=8.5$

Q4

A researcher conducts a study by taking independent random samples. Assuming the experiment meets the conditions of the Law of Large Numbers, which sample mean is the closest to the value of the population mean?

n	mean
20	4.77
50	5.16
100	4.97
200	5.01

1. 4.77
2. 5.16
3. 4.97
4. 5.01

Answer

4

Nice job! The Law of Large Numbers states that as the sample size increases, the sample mean approaches the population mean if certain conditions are satisfied. The conditions that must be met are the following:

1. The sample is randomly drawn.
2. The sample size must be sufficiently large.
3. Each observation must be independent of the others.

Q5

Which of the following best describes the Central Limit Theorem?

1. The Central Limit Theorem states that the mean of a population is always normally distributed.
2. The Central Limit Theorem states that, under certain conditions, the sample mean approaches the population mean as the sample size increases.
3. The Central Limit Theorem states that, under certain conditions, as the sample size increases, the sampling distribution of the mean approaches a normal distribution, regardless of the distribution of the population.
4. The Central Limit Theorem states that as the sample size increases, the variance of the population decreases.

Answer

3

Nice job! The Central Limit Theorem states that the sample means will be normally distributed if you sample several times from a population. However, for this theorem to apply, you must use large sample sizes.

All the information provided is based on the Probability & Statistics for Machine Learning & Data Science | Coursera from DeepLearning.AI