Lesson test: From probability to inference

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From probability to inference

1.[2p]
What distinguishes a statistical problem from a probability problem?

The model is unknown and the data is given, so the reasoning runs from outcome back to cause

Correct

The data is unknown and the model is given, so the reasoning runs from cause to outcome

The answer is: The model is unknown and the data is given, so the reasoning runs from outcome back to cause

Statistical problems concern populations and probability problems concern samples

The answer is: The model is unknown and the data is given, so the reasoning runs from outcome back to cause

Statistical problems allow no randomness, since the data has already been observed

The answer is: The model is unknown and the data is given, so the reasoning runs from outcome back to cause

2.[2p]
Match each symbol to what it is.

$μ$
$\overline{x}$
$p$
$\hat{p}$

a population proportion
a population mean, fixed and unknown
a sample proportion
a sample mean, computed and known

Show the answer

$μ$ : a population mean, fixed and unknown $\overline{x}$ : a sample mean, computed and known $p$ : a population proportion $\hat{p}$ : a sample proportion

3.[2p]
A fair die has population standard deviation $1.7078$ . What is the standard deviation of the mean of 40 rolls?

CorrectNot quite: 0.270

4.[2p]
Collecting more data reduces both the sampling error and the bias of an estimate.

True

The answer is: False

False

Correct

5.[3p]
How large a sample makes $1.96 \sqrt{p (1 - p) / n}$ equal to $0.01$ when $p = 0.5$ ?

CorrectNot quite: 9604

6.[2p]
In a survey of 1000 people, 400 answer yes. What is the standard error of $\hat{p}$ , to four decimal places?

CorrectNot quite: 0.0155

7.[3p]
Which of these are true of the sampling distribution of $\overline{X}$ ?

Select all that apply

It is the distribution of the values $\overline{X}$ takes across all possible samples

Correct

Its standard deviation falls as $1 / \sqrt{n}$

Correct

It exists whether or not anybody computes it

Correct

Its mean depends on which sample was actually drawn

The answer is: It is the distribution of the values $\overline{X}$ takes across all possible samples, Its standard deviation falls as $1 / \sqrt{n}$ , It exists whether or not anybody computes it

8.[2p]
A national poll of 1000 people gives a margin of about 3 points. Why does the size of the country barely matter?

The finite population correction $\sqrt{(N - n) / (N - 1)}$ is essentially 1 whenever $N$ is much larger than $n$

Correct

Because polls are always conducted on a fixed percentage of the population

The answer is: The finite population correction $\sqrt{(N - n) / (N - 1)}$ is essentially 1 whenever $N$ is much larger than $n$

Because the margin of error is defined without reference to the data

The answer is: The finite population correction $\sqrt{(N - n) / (N - 1)}$ is essentially 1 whenever $N$ is much larger than $n$

Because larger countries have more variable opinions, which cancels the effect

The answer is: The finite population correction $\sqrt{(N - n) / (N - 1)}$ is essentially 1 whenever $N$ is much larger than $n$

9.[2p]
A scale reads 0.8 kg heavy and its readings vary by 0.3 kg. Put these sample sizes in order of the standard error of the mean reading, largest first.

10000 readings
4 readings
100 readings
25 readings

Show the answer

a, b, c, d

1.[2p] What distinguishes a statistical problem from a probability problem?

2.[2p] Match each symbol to what it is.

3.[2p] A fair die has population standard deviation 1.7078. What is the standard deviation of the mean of 40 rolls?

4.[2p] Collecting more data reduces both the sampling error and the bias of an estimate.

5.[3p] How large a sample makes 1.96p(1−p)/n equal to 0.01 when p=0.5?

6.[2p] In a survey of 1000 people, 400 answer yes. What is the standard error of pˆ, to four decimal places?

7.[3p] Which of these are true of the sampling distribution of X‾?

8.[2p] A national poll of 1000 people gives a margin of about 3 points. Why does the size of the country barely matter?

9.[2p] A scale reads 0.8 kg heavy and its readings vary by 0.3 kg. Put these sample sizes in order of the standard error of the mean reading, largest first.

1.[2p]
What distinguishes a statistical problem from a probability problem?

2.[2p]
Match each symbol to what it is.

3.[2p]
A fair die has population standard deviation $1.7078$ . What is the standard deviation of the mean of 40 rolls?

4.[2p]
Collecting more data reduces both the sampling error and the bias of an estimate.

5.[3p]
How large a sample makes $1.96 \sqrt{p (1 - p) / n}$ equal to $0.01$ when $p = 0.5$ ?

6.[2p]
In a survey of 1000 people, 400 answer yes. What is the standard error of $\hat{p}$ , to four decimal places?

7.[3p]
Which of these are true of the sampling distribution of $\overline{X}$ ?

8.[2p]
A national poll of 1000 people gives a margin of about 3 points. Why does the size of the country barely matter?

9.[2p]
A scale reads 0.8 kg heavy and its readings vary by 0.3 kg. Put these sample sizes in order of the standard error of the mean reading, largest first.