module 6

Question 1

population parameters

Answer 1

• attributes of the statistical population
• the values are fixed
• labeled using the greek alphabet, such as μ for the mean or σ for the standard deviation

Question 2

what sit called when descriptive statistics of a sample become the population parameters of the statistical population.

Answer 2

estimation

Question 2

sampling distribution

Answer 2

• distribution of some descriptive stat that would emerge if one were to repeatedly draw samples from the stat pop

Question 3

What effect does sample size have on the characteristics of the sampling distribution

Answer 3

Shape independence in the sampling distribution only holds if the sample size is sufficiently large. If your statistical population is already symmetrical and roughly bell-shaped, then sample sizes of n=5 are enough to ensure that the shape of the sampling distribution is independent of the statistical population.

Question 4

What are the characteristics of a sampling distribution?

Answer 4

1. The shape of a sampling distribution is independent of the statistical population so long as the sample size is sufficiently large.
2. The variance of a sampling distribution increases as the number of sampling units in the sample decreases. As the size of a sample increases, the variance of the sampling distribution decreases.

Question 5

Central limit theorem

Answer 5

allows us to calculate the mean and standard deviation of the sampling distribution without the need to construct it.

Question 6

What are the two key characterisicts of sampling distributions?

Answer 6

1. that a sampling distribution has a bell-shape that is independent of the statistical population.
2. that the variance of a sampling distribution decreases as the sample size increases.

Question 7

Standard error

Answer 7

is the standard deviation of the sampling distribution.

Question 8

Student’s t-distribution

Answer 8

is a probability distribution used to describe the sampling distribution when the parameters of the statistical population are estimated from a sample.

Question 9

Standard error

Answer 9

is the standard deviation of the sampling distribution. SE=σ/√n

Question 10

What does this equation mean?
SE=σ/√n

Answer 10

The central limit theorem adds that the standard error (SE) is the standard deviation of the statistical population divided by the square-root of the sample size.

Question 11

What is a chain of inference?

Answer 11

is that a single sample from a statistical population is enough for us to estimate the sampling distribution.

Question 12

What is is the problem with central limit theorum?

Answer 12

The problem is that we do not know the value of the standard deviation of the statistical population in practice. Rather, we need to estimate it from our sample. This reality means we have greater uncertainty in the sampling distribution than would be suggested by the Normal distribution.

Question 13

T-distribution

Answer 13

is a probability distribution used to describe the sampling distribution when the parameters of the statistical population are estimated from a sample.

Question 14

Confidence intervals

Answer 14

The range over a sampling distribution that brackets the centre-most probability of interest. They are a statement of what future samples will look like. Confidence intervals are derived from sampling distributions, and they describe the range over the x-axis that brackets a specific probability of finding a value from a new sample.

Question 15

What is the degree of uncertainty?

Answer 15

The degree of uncertainty is how much the descriptive statistic is expected to change if we repeated the sampling process.

Question 16

What are the two steps of confidence intervals?

Answer 16

1. Find the intervals on the standardized scale: The first step is to use the t-distribution to find the locations on the x-axis that correspond to the probability of interest. These are standardized t-scores, which we can label tL and tU to represent the lower and upper confidence interval on the standardized scale.
2. Convert to the raw scale The second step is to convert the standardized t-scores to the raw scale. We will use xL and xU to represent the lower and upper confidence intervals on the raw scale.