A public health agency claimed last year that the proportion of children vaccinated for measles met their goal of 85%, however, they want to test if the current proportion falls shy of that goal. What are the Type I & Type II Errors? Which is more serious?
Table of contents
- 1. Intro to Stats and Collecting Data1h 14m
- 2. Describing Data with Tables and Graphs1h 55m
- 3. Describing Data Numerically2h 5m
- 4. Probability2h 16m
- 5. Binomial Distribution & Discrete Random Variables3h 6m
- 6. Normal Distribution and Continuous Random Variables2h 11m
- 7. Sampling Distributions & Confidence Intervals: Mean3h 23m
- Sampling Distribution of the Sample Mean and Central Limit Theorem19m
- Distribution of Sample Mean - Excel23m
- Introduction to Confidence Intervals15m
- Confidence Intervals for Population Mean1h 18m
- Determining the Minimum Sample Size Required12m
- Finding Probabilities and T Critical Values - Excel28m
- Confidence Intervals for Population Means - Excel25m
- 8. Sampling Distributions & Confidence Intervals: Proportion2h 10m
- 9. Hypothesis Testing for One Sample5h 8m
- Steps in Hypothesis Testing1h 6m
- Performing Hypothesis Tests: Means1h 4m
- Hypothesis Testing: Means - Excel42m
- Performing Hypothesis Tests: Proportions37m
- Hypothesis Testing: Proportions - Excel27m
- Performing Hypothesis Tests: Variance12m
- Critical Values and Rejection Regions28m
- Link Between Confidence Intervals and Hypothesis Testing12m
- Type I & Type II Errors16m
- 10. Hypothesis Testing for Two Samples5h 37m
- Two Proportions1h 13m
- Two Proportions Hypothesis Test - Excel28m
- Two Means - Unknown, Unequal Variance1h 3m
- Two Means - Unknown Variances Hypothesis Test - Excel12m
- Two Means - Unknown, Equal Variance15m
- Two Means - Unknown, Equal Variances Hypothesis Test - Excel9m
- Two Means - Known Variance12m
- Two Means - Sigma Known Hypothesis Test - Excel21m
- Two Means - Matched Pairs (Dependent Samples)42m
- Matched Pairs Hypothesis Test - Excel12m
- Two Variances and F Distribution29m
- Two Variances - Graphing Calculator16m
- 11. Correlation1h 24m
- 12. Regression3h 33m
- Linear Regression & Least Squares Method26m
- Residuals12m
- Coefficient of Determination12m
- Regression Line Equation and Coefficient of Determination - Excel8m
- Finding Residuals and Creating Residual Plots - Excel11m
- Inferences for Slope31m
- Enabling Data Analysis Toolpak1m
- Regression Readout of the Data Analysis Toolpak - Excel21m
- Prediction Intervals13m
- Prediction Intervals - Excel19m
- Multiple Regression - Excel29m
- Quadratic Regression15m
- Quadratic Regression - Excel10m
- 13. Chi-Square Tests & Goodness of Fit2h 21m
- 14. ANOVA2h 28m
9. Hypothesis Testing for One Sample
Type I & Type II Errors
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Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
Describe a Type I & Type II Error for each scenario.
A new cancer screening test reports whether a patient has cancer.
A
Type I: The test is positive but the patient doesn't have cancer.
Type II: The test is negative but the patient has cancer.
B
Type I: The test is negative but the patient has cancer.
Type II: The test is positive but the patient doesn't have cancer.
C
Type I: The test is positive and the patient has cancer.
Type II: The test is negative and the patient doesn't have cancer.
D
Type I: The test is negative and the patient doesn't have cancer.
Type II: The test is positive and the patient has cancer.
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Verified step by step guidance1
Step 1: Identify the null hypothesis (H0) and the alternative hypothesis (H1) based on the problem context. Here, the hypotheses relate to the parameter P, where H0: P = 0.85 and H1: P ≠ 0.85 (or specifically P > 0.85 or P < 0.85 depending on the scenario).
Step 2: Understand what a Type I error means: it occurs when we reject the null hypothesis H0 when it is actually true. In this context, a Type I error would be concluding that P is different from 0.85 (e.g., P > 0.85 or P < 0.85) when in fact P = 0.85.
Step 3: Understand what a Type II error means: it occurs when we fail to reject the null hypothesis H0 when the alternative hypothesis H1 is true. Here, a Type II error would be concluding that P = 0.85 when in fact P is greater than or less than 0.85.
Step 4: For each scenario, match the statements to the errors: for example, 'We conclude that P < 0.85 when actually P = 0.85' is a Type I error because we rejected H0 incorrectly; 'We conclude that P = 0.85 when actually P < 0.85' is a Type II error because we failed to reject H0 when it was false.
Step 5: Finally, consider the seriousness of the errors as given. If Type I is more serious, focus on minimizing false positives (rejecting H0 incorrectly). If Type II is more serious, focus on minimizing false negatives (failing to reject H0 when it is false). This helps interpret which error corresponds to which conclusion in the problem.
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Multiple Choice
Type I & Type II Errors practice set

