Lesson test: The sampling distribution

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The sampling distribution

1.[1p]
A population has $σ = 12$ . What is the standard error of the mean of a simple random sample of 36?

CorrectNot quite: 2

2.[2p]
For the same population, how many observations bring the standard error down to 0.5?

CorrectNot quite: 576

3.[2p]
What does "standard error of the mean" refer to?

The standard deviation of the sampling distribution of $\overline{X}$

Correct

The standard deviation of the observations in the sample

The answer is: The standard deviation of the sampling distribution of $\bar{X}$

The difference between $\overline{x}$ and $μ$ for this sample

The answer is: The standard deviation of the sampling distribution of $\bar{X}$

The bias introduced by the sampling design

The answer is: The standard deviation of the sampling distribution of $\bar{X}$

4.[1p]
The central limit theorem requires the population distribution to be normal.

True

The answer is: False

False

Correct

5.[3p]
Service times have mean 4 minutes and standard deviation 4 minutes. Using the normal approximation, what is $P (\overline{X} > 5)$ for a sample of 50, to three decimal places?

CorrectNot quite: 0.039

6.[3p]
Match each distribution to what it describes.

Population distribution
Sample distribution
Sampling distribution
Standard error

the spread of the sampling distribution
the batch actually collected
the estimate across repetitions
the values in the world

Show the answer

Population distribution: the values in the world Sample distribution: the batch actually collected Sampling distribution: the estimate across repetitions Standard error: the spread of the sampling distribution

7.[3p]
Which assumptions are used in deriving $Var (\overline{X}) = σ^{2} / n$ ?

Select all that apply

The observations are independent

Correct

The population variance $σ^{2}$ is finite

Correct

The population is symmetric

The answer is: The observations are independent, The population variance $\sigma^2$ is finite

The sample size exceeds 30

The answer is: The observations are independent, The population variance $\sigma^2$ is finite

8.[2p]
With $p = 0.1$ and $n = 30$ , a nominal 5 per cent normal tail is actually 7.3 per cent. Why?

$n p = 3$ is too small, so the binomial is squashed against zero and far from normal

Correct

The central limit theorem does not apply to discrete variables

The answer is: $np = 3$ is too small, so the binomial is squashed against zero and far from normal

The standard error formula is wrong for proportions

The answer is: $np = 3$ is too small, so the binomial is squashed against zero and far from normal

Thirty is below the minimum sample size for any statistic

The answer is: $np = 3$ is too small, so the binomial is squashed against zero and far from normal

9.[2p]
A sample of 100 has $s = 3.2$ . What is the estimated standard error of the mean?

CorrectNot quite: 0.32

1.[1p] A population has σ=12. What is the standard error of the mean of a simple random sample of 36?

2.[2p] For the same population, how many observations bring the standard error down to 0.5?

3.[2p] What does "standard error of the mean" refer to?

4.[1p] The central limit theorem requires the population distribution to be normal.

5.[3p] Service times have mean 4 minutes and standard deviation 4 minutes. Using the normal approximation, what is P(X‾>5) for a sample of 50, to three decimal places?

6.[3p] Match each distribution to what it describes.

7.[3p] Which assumptions are used in deriving Var(X‾)=σ2/n?

8.[2p] With p=0.1 and n=30, a nominal 5 per cent normal tail is actually 7.3 per cent. Why?

9.[2p] A sample of 100 has s=3.2. What is the estimated standard error of the mean?

1.[1p]
A population has $σ = 12$ . What is the standard error of the mean of a simple random sample of 36?

2.[2p]
For the same population, how many observations bring the standard error down to 0.5?

3.[2p]
What does "standard error of the mean" refer to?

4.[1p]
The central limit theorem requires the population distribution to be normal.

5.[3p]
Service times have mean 4 minutes and standard deviation 4 minutes. Using the normal approximation, what is $P (\overline{X} > 5)$ for a sample of 50, to three decimal places?

6.[3p]
Match each distribution to what it describes.

7.[3p]
Which assumptions are used in deriving $Var (\overline{X}) = σ^{2} / n$ ?

8.[2p]
With $p = 0.1$ and $n = 30$ , a nominal 5 per cent normal tail is actually 7.3 per cent. Why?

9.[2p]
A sample of 100 has $s = 3.2$ . What is the estimated standard error of the mean?