Statistical Estimation and the Law of Large Numbers

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Questions 1-3

Question 1.

Yield is to be measured as the response variable. Is it categorical or quantitative?

Quantitative

Categorical

Incorrect. Bushels per acre is a quantitative response variable.

Correct. Bushels per acre is a quantitative response variable.

Incorrect. Try again.

Questions 4-7

104

Question 4.

True or false: $\overline{x}$ almost always equals µ.

False

True

Incorrect.

$\overline{x}$ almost never equals µ. This is one reason why we need sampling distributions.

Correct.

$\overline{x}$ almost never equals µ. This is one reason why we need sampling distributions.

Incorrect. Try again.

Question 5.

True or false: We should get the same value for $\overline{x}$ from most of our samples.

False

True

Incorrect. A different sample will almost always give a different value for

$\overline{x}$ . This is another reason why we need sampling distributions.

Correct. A different sample will almost always give a different value for

$\overline{x}$ . This is another reason why we need sampling distributions.

Incorrect. Try again.

Question 6.

True or false: The value of $\overline{x}$ varies (changes) from one sample to the next.

False

True

Incorrect. Because

$\overline{x}$ varies from one sample to the next, we usually get a different value for

$\overline{x}$ for each sample.

Correct. Because

$\overline{x}$ varies from one sample to the next, we usually get a different value for

$\overline{x}$ for each sample.

Incorrect. Try again.

Question 7.

True or false: The larger the sample size, the farther $\overline{x}$ will be from µ.

False

True

Incorrect. The opposite is true; the larger the sample, the closer

$\overline{x}$ should be to µ. If you think about it, as we continue to increase sample size, we will eventually sample the entire population and the mean with equal µ. This fact has a name as you will see in the next slide.

Correct. The opposite is true; the larger the sample, the closer

Incorrect. Try again.

Question 8

138

Question 8.

What is the basic idea of the law of large numbers?

The larger the population size, the more individuals you need to sample.

The more data you sample, the larger the standard deviation gets.

The larger the sample size, the closer the sample mean is to the population mean.

Incorrect. Answers B and C are false statements. As you increase the sample size, you sample more and more of the population. Eventually, you will sample the entire population so the mean will equal the population mean.

Correct. Answers B and C are false statements. As you increase the sample size, you sample more and more of the population. Eventually, you will sample the entire population so the mean will equal the population mean.

Incorrect. Try again.

StatTutor Lesson - Statistical Estimation and the Law of Large Numbers

Questions 1-3

Question 1.

Question 2.

Question 3.

Questions 4-7

Question 4.

Question 5.

Question 6.

Question 7.

Question 8

Question 8.