Activity 22

MATH 216: Statistical Thinking

Activity 1: Hypothesis Setup & Directionality

Scenario: Park benches allegedly fail before 5-year warranty (vendor claims μ ≥ 5 years).

Step 1: Frame Hypotheses

“Which claim becomes our default assumption (H₀)? Should our alternative hypothesis be left or right-tailed?”

Step 2: Direction Reasoning

“Why left-tailed?

Step 3: Error Contextualization

“Type I Error ($\alpha =0.05$):

Type II Error:

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Activity 2: Test Statistic & Distribution Choice

Scenario: Sample data shows $\overline{x}=4.2$ years, $s=1.1$, $n=35$

Step 1: Distribution Selection

Z vs T:

Step 2: Standard Error Calculation

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n <- 35

se <- 1.1/sqrt(35) # Standard Error

round(se, 3)

_webr_editor_1 = Object {code: null, options: Object, indicator: it}

Step 3: t-Score Computation

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t_score <- (4.2 - 5)/se

round(t_score, 2)

_webr_editor_2 = Object {code: null, options: Object, indicator: it}

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Activity 3: Rejection Regions & Decision Making

Scenario: Critical t-value = -1.69 ($df=34,\alpha =0.05$)

Step 1: Visualize Rejection Region

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curve(dt(x, df=34), from=-5, to=3, main="t-Distribution (df=34)")

abline(v=qt(0.05, 34), col="red", lwd=2)

text(-2, 0.3, "Rejection Region\nα = 0.05", col="red")

_webr_editor_3 = Object {code: null, options: Object, indicator: it}

Step 2: Decision Rule

Step 3: Formal Conclusion

Step 4: Error Accountability

Downloading webR