Table of contents
- 1. Intro to Stats and Collecting Data55m
- 2. Describing Data with Tables and Graphs1h 55m
- 3. Describing Data Numerically1h 45m
- 4. Probability2h 16m
- 5. Binomial Distribution & Discrete Random Variables2h 33m
- 6. Normal Distribution and Continuous Random Variables1h 38m
- 7. Sampling Distributions & Confidence Intervals: Mean1h 3m
- 8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- 9. Hypothesis Testing for One Sample1h 1m
- 10. Hypothesis Testing for Two Samples2h 8m
- 11. Correlation48m
- 12. Regression1h 4m
- 13. Chi-Square Tests & Goodness of Fit1h 20m
- 14. ANOVA1h 0m
10. Hypothesis Testing for Two Samples
Two Proportions
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Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
A human resources department is comparing two employee training programs to see if they lead to different pass rates on a required certification exam. They randomly select two groups of employees. In Program A, 16 out of 20 employees passed the exam. In Program B, 30 out of 40 employees passed. Are the basic conditions met to conduct a 2-proportion hypothesis test?
A
Yes, the basic conditions are met.
B
No, the basic conditions are not met.
C
There is not enough information to answer the question.

1
Step 1: Understand the problem. The goal is to determine whether the basic conditions for conducting a 2-proportion hypothesis test are met. A 2-proportion hypothesis test compares the proportions of successes (e.g., pass rates) between two groups.
Step 2: Recall the basic conditions for a 2-proportion hypothesis test. These include: (1) Random sampling from each population, (2) Independence between the two groups, and (3) Sufficiently large sample sizes such that the expected number of successes and failures in each group is at least 5. This is often checked using the formulas: nâ‚p̂₠≥ 5, nâ‚(1 - pÌ‚â‚) ≥ 5, nâ‚‚p̂₂ ≥ 5, and nâ‚‚(1 - p̂₂) ≥ 5, where nâ‚ and nâ‚‚ are the sample sizes, and p̂₠and p̂₂ are the sample proportions.
Step 3: Calculate the sample proportions for each group. For Program A, the sample proportion is p̂₠= 16/20. For Program B, the sample proportion is p̂₂ = 30/40. These proportions represent the pass rates for each program.
Step 4: Check the expected number of successes and failures for each group. For Program A, calculate nâ‚p̂₠(expected successes) and nâ‚(1 - pÌ‚â‚) (expected failures). For Program B, calculate nâ‚‚p̂₂ (expected successes) and nâ‚‚(1 - p̂₂) (expected failures). Verify that all these values are at least 5.
Step 5: Evaluate whether the other conditions (random sampling and independence) are met. If all conditions are satisfied, the test can proceed. If any condition is not met, the test cannot be conducted.
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