12A/B/C

Skill or Concept: I can . . . Questions to check your understanding Rating
from 1 to 5
Use the DCMP Normal Distribution tool to calculate normal probabilities. 1, 5
Simulate random samples from a population using the DCMP Sampling Distribution of the Sample Mean (Continuous Population) tool. 2, 3
Find the mean and standard deviation of the sampling distribution of the sample mean. 4
Use the mean and standard deviation of the sampling distribution of the sample mean to calculate and interpret a z-score for a sample mean. 6

A woman standing with a suitcase looking out over a river in front of a city. A plot labeled “Population Distribution” with a subheading reading mu = 4.67, sigma = 2.61.” The x-axis is labeled in increments of 1 and the y-axis is labeled “P(X=x).” There is a point labeled mu at 4.68. It is skewed left.

Sample 2 Sample 3 Sample 4 Sample 5
Skill or Concept: I can . . . Questions to check your understanding Rating
from 1 to 5
Calculate and interpret a standardized sample mean. 2, Parts A and B

5
Calculate and interpret the standard deviation of a sample mean. 2, Part C

3, 4
Calculate probabilities involving standardized statistics. 6

A man wearing an apron smiling in a cafe. A curve labeled “Standardized statistic.” There is a legend showing that the dashed line indicates “t with 3 df,” the dotted line indicates “t with 8 df,” the dotted and dashed line indicates “t with 14 df,” and the solid line indicates “Standard normal.” For all three lines, there is a peak at approximately 0. Compared to the solid line, the lower the degree of freedom is, the lower the values are near the peak and the higher they are near the edges.

Skill or Concept: I can . . . Questions to check your understanding Rating
from 1 to 5
Identify the population of interest in a research study. 1, Part A

2, Part A
Use information about a sample to assess whether it is reasonable to think a population is approximately normal in a given context. 1, Parts C and D

2, Parts C and D
Calculate and interpret the standard error of the sample mean. 1, Parts E through G

2, Parts E through G

A number line labeled in increments of 1 from 41 to 59, showing a thick blue line from 42 to 58. A number line labeled in increments of 1 from 9 to 14 showing a thick blue line from approximately 9.5 to 13.5. Several coins and some cash, as well as a paper that reads “Student Debt.” There is a jagged vertical arrow. A histogram labeled “Hours Watching TV (2018)” on the horizontal axis and “Frequency” on the vertical axis. For 0, the frequency is approximately 140. For 1, the frequency is approximately 350. For 2, the frequency is approximately 375. For 3, the frequency is approximately 225. For 4, the frequency is approximately 175. For 5, the frequency is approximately 100. For 6, the frequency is approximately 70. For 7, the frequency is approximately 20. For 8, the frequency is approximately 50. For 9, the frequency is approximately 10. For 10, the frequency is approximately 40. For 12, the frequency is approximately 30. For 14, the frequency is approximately 1. For 15, the frequency is approximately 5. For 16, the frequency is approximately 3. For 20, the frequency is approximately 7. For 24, the frequency is approximately 6.

Glossary 12A

z-score
a measure of a value’s distance from the mean in units of standard deviation, also called standardized score.
sampling distribution
the probability distribution of a sample statistic, such as a sample mean or sample proportion, as it varies from sample to sample.
Central Limit Theorem
as the sample size gets larger, the distribution of the sample mean will become closer to a normal distribution.

Glossary 12B

sampling variability
the tendency of samples to have different statistics (means, proportions) than the population as a whole due to randomness.
sampling distribution
the distribution of a sample statistic, such as a sample mean or sample proportion, as it varies from sample to sample.
standard error
an estimate of the standard deviation of a statistic.
standard normal distribution.
a normal distribution with a mean of 0 and a standard deviation of 1.
t-score
no description

Glossary 12C

one-sample t interval
no description