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
4. Probability
Basic Concepts of Probability
Problem 5.1.20d
Textbook Question
Using Probabilities for Significant Events
d. Is 1 a significantly low number of matches? Why or why not?

1
Step 1: Understand the concept of 'significantly low' in statistics. A number is considered significantly low if its probability of occurrence is very small, typically less than or equal to 0.05 (5%). This threshold is often used in hypothesis testing.
Step 2: Identify the probability distribution that governs the number of matches in the given scenario. For example, it could be a binomial distribution, Poisson distribution, or another relevant model depending on the context of the problem.
Step 3: Calculate the probability of observing exactly 1 match using the appropriate probability formula for the identified distribution. For instance, if it's a binomial distribution, use the formula: , where n is the number of trials, k is the number of successes, and p is the probability of success.
Step 4: Compare the calculated probability of observing 1 match to the significance threshold (e.g., 0.05). If the probability is less than or equal to the threshold, then 1 match is considered significantly low. Otherwise, it is not.
Step 5: Provide reasoning based on the comparison. If the probability is significantly low, explain that this indicates the event is unlikely to occur under normal circumstances. If it is not significantly low, explain that the event is within the range of expected outcomes.

This video solution was recommended by our tutors as helpful for the problem above
Video duration:
2mPlay a video:
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Significance Level
The significance level, often denoted as alpha (α), is a threshold used in hypothesis testing to determine whether to reject the null hypothesis. Commonly set at 0.05, it represents the probability of making a Type I error, which occurs when a true null hypothesis is incorrectly rejected. Understanding this concept is crucial for assessing whether a result, such as the number of matches, is statistically significant.
Recommended video:
Guided course
Step 4: State Conclusion Example 4
Statistical Power
Statistical power is the probability that a test will correctly reject a false null hypothesis. It is influenced by the sample size, effect size, and significance level. A low number of matches, like 1, may lead to low power, making it difficult to detect a true effect if one exists. This concept helps in evaluating whether the observed number of matches is sufficient to draw meaningful conclusions.
Recommended video:
Guided course
Parameters vs. Statistics
Contextual Interpretation of Data
Contextual interpretation involves analyzing data within the framework of the specific situation or experiment. In this case, determining whether 1 match is significantly low requires understanding the expected number of matches based on prior data or theoretical models. This concept emphasizes that statistical results should not be viewed in isolation but rather in relation to the broader context of the study.
Recommended video:
Guided course
Visualizing Qualitative vs. Quantitative Data
Watch next
Master Introduction to Probability with a bite sized video explanation from Patrick
Start learningRelated Videos
Related Practice