Statistics
Fall Semester | |||||
Unit Title | Unit 1: Random Sampling and Experimental Design | Unit 2: Univariate Data | Unit 3: Normal Distribution | Unit 4: Linearity | Unit 5: Probability and Simulations |
Time | ~ 4 weeks | ~ 5 weeks | ~ 3 weeks | ~ 3 weeks | ~ 3 weeks |
Understandings | Random sampling is used to avoid bias. Simple random sampling, stratified random sampling, cluster sampling, and systematic sampling with a random start are all valid sampling methods.
Experiments should identify the experimental units, explanatory variables (factors), treatments, and response variables.
A statistical sample is used to draw a conclusion about a population parameter. sample statistics must be gathered randomly to make a valid conclusion about a population parameter.
valid sampling methods are used to avoid bias and underrepresentation of certain groups. poorly-designed sampling methods can cause bias and unreasonable conclusions.
| Measures of variability calculated according to a mathematical model will approximate the true variability of a population distribution.
Distributions of quantitative data can be compared using dotplots, stemplots, boxplots, or histograms. Parameters include all of the elements from a population while sample statistics consists of one or more observations from the population. Appropriate graphs and numerical summaries must be used to compare distributions of quantitative variables.
Graphical data can be displayed using bar graphs, pie charts, and frequency tables. There is a method to analyze marginal and conditional distributions using two-way tables.
| The Empirical Rule is a statistical model that closely approximates the mathematical model of the Normal distribution regarding shape, center, and variability.
Any specific Normal curve is completely described by giving its mean and its standard deviation . Normal distributions are used to compute probabilities. Normal distributions are used to calculate extreme values.
Normal distributions are good models for many distributions of real data, are good approximations of probabilities for many kinds of chance outcomes, and are the bases of many statistical inference procedures. | The strength of a linear relationship increases as the value of r, the correlation variable, moves away from 0 toward either -1 or 1. A regression line is used to summarize the overall pattern of a scatterplot that shows a linear relationship.
A least-squares regression line is based on residuals and makes the sum of the squared residuals as small as possible.
Least-squares regression lines and median-median regression lines may differ quite a bit if there are any influential points in the data.
| Probability is the single value representing the proportion of times that a specific outcome occurs as we observe more and more repetitions of any chance process. In a very long series of repetitions, the proportion of times that a specific outcome occurs approaches a single value.
The general multiplication rule is useful when a chance process involves a sequence of outcomes. If two events have no outcomes in common, the probability that one or the other occurs is the sum of their individual probabilities. If two events have some outcomes in common, the probability that one or the other occurs requires use of the general addition rule.
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TEKS | S.2 A, B, C, D, E, F, G | S.3 A,B, C S.4 A, B, C, D, E, F | S.3 A,B, D S.4 B, C, E | S.7 A, B, C, D, E, F | S.5 A, B, C |
Process Standards | 1 A, B, C, D, E, F, G | ||||
Statistics
Spring Semester | ||||||
Unit Title | Unit 6: Random Variables and Probability Distributions | Unit 7: Sample Proportions and Means | Unit 8: Estimating with Confidence Intervals | Unit 9: Testing a Claim | Unit 10: Comparing Two Populations | Unit 11: Chi-Square |
Time | ~ 2 weeks | ~ 3 weeks | ~ 3 weeks | ~ 2 weeks | ~ 3 weeks | ~ 4 weeks |
Understandings | The probability model for a random variable is its probability distribution. Every probability is a number between 0 and 1, inclusive. All possible probabilities for a discrete random variable add up to one. Probability distribution is used to answer questions about possible values of a random variable.
| The mean of the sampling distribution of the sample proportion is equal to the population proportion. The mean of the sampling distribution of a sample mean is equal to the population mean.
The value of the standard deviation for proportional data depends on both sample size and population proportion. The value of the sample standard deviation for means data depends upon the sample size and the population standard deviation.
| Clearly-defined levels of confidence are necessary to create an understandable confidence interval. The mean and standard error of a sample are crucial values needed for the construction of a confidence interval.
The larger the sample size, the smaller the measure of error. The greater the level of confidence, the wider the confidence interval; the smaller the level of confidence, the narrower the confidence interval.
| A sample that is more than 2 standard deviations away from the mean in a sampling distribution usually provides evidence against the null hypothesis.
Correct hypotheses for significance tests about a population proportion or mean are stated in a certain way: The null hypothesis has the form H0:parameter = value and the alternative hypothesis has one of the forms Ha:parameter < value, Ha:parameter > value, or Ha:parameter ≠ value.
The significance level of any fixed-level test is the probability of a Type I error. The severity of the impact of a Type I or Type II error is different for each situation. | When comparing populations the appropriate tests must be used.
Confidence intervals, hypothesis and significance tests are critical in comparing populations. | Categorical variables assign labels that place individuals into particular groups. Quantitative variables take numerical values for which it makes sense to find an average.
the distribution of categorical data from a data set can be compared using two-way tables and bar graphs. appropriate graphs and statistical values must be used to compare/contrast the distribution of a data set.
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TEKS | S.5 A, C | S.2 D S.4 B, C S.5 D | S.6 A, B, C, D, E | S.6 F, G, H, I, J | S.6 A, B, C, D, E, F, G, H, I, J | S.4 B, D S.6 G, I |
Process Standards | S.1 A, B, C, D, E, F, G | |||||