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US-VA

Math

Virginia Math

Probability and Statistics: Inferential Statistics

PS.IS.1

The student will apply properties of sampling distributions and inference procedures to make decisions about population proportions.

PS.IS.1.a

Describe the shape, center, and spread of the sampling distribution of a proportion within the context of a problem.
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PS.IS.1.b

Given a problem, construct a one sample 𝑧 confidence interval:

PS.IS.1.b.i

identify the basic conditions for inference: random sample, independence, and normality;
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PS.IS.1.b.ii

calculate a confidence interval using technology; and
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PS.IS.1.b.iii

interpret the interval within the context of the problem.
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PS.IS.1.c

Explain how changes in confidence level and sample size affect width of the confidence interval and margin of error.
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PS.IS.1.d

Calculate and interpret a point estimate and margin of error of a confidence interval for a proportion within the context of the problem.
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PS.IS.1.e

Explain how and why the hypothesis testing procedure allows one to reach a statistical decision.
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PS.IS.1.f

Given a problem, apply the one sample 𝑧 hypothesis testing procedures:

PS.IS.1.f.i

construct appropriate null and alternate hypotheses;
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PS.IS.1.f.ii

identify the basic conditions for inference: random sample; independence, and normality;
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PS.IS.1.f.iii

calculate and interpret the 𝑝-value using technology;
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PS.IS.1.f.iv

determine and justify whether to reject the null hypothesis; and
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PS.IS.1.f.v

interpret the results within the context of the problem.
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PS.IS.1.g

Use the statistical cycle to plan and conduct a statistical study about a proportion to answer a question or address a problem with inference.
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PS.IS.2

The student will apply properties of sampling distributions and inference procedures to make decisions about populations.

PS.IS.2.a

Describe the shape, center, and spread of the sampling distribution of a mean within the context of a problem.

PS.IS.2.b

Calculate and interpret a point estimate and a margin of error for a confidence interval of a mean within the context of a problem.
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PS.IS.2.c

Describe the use of the Central Limit Theorem in satisfying the assumptions and conditions for inference about a mean.
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PS.IS.2.d

Identify the properties of a 𝑡 distribution.
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PS.IS.2.e

Given a problem, construct a one sample 𝑡 confidence interval:

PS.IS.2.e.i

identify the basic conditions for inference: random sample, independence, and approximate normality;
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PS.IS.2.e.ii

calculate a confidence interval using technology; and
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PS.IS.2.e.iii

interpret the interval within the context of the problem.
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PS.IS.2.f

Given a problem, apply the one sample 𝑡 hypothesis testing procedures:

PS.IS.2.f.i

construct appropriate null and alternate hypotheses;
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PS.IS.2.f.ii

identify the basic conditions for inference: random sample, independence, and approximate normality;
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PS.IS.2.f.iii

calculate and interpret the 𝑝 value using technology;
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PS.IS.2.f.iv

determine and justify whether to reject the null hypothesis; and
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PS.IS.2.f.v

interpret the results within the context of the problem.
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