Chapter 8 Quiz: Hypothesis Testing and Statistical Significance

Instructions: Answer all 25 questions. Each question has one best answer unless otherwise noted. After completing the quiz, check your answers using the hidden answer key at the end.

Question 1

In the context of evaluating a sports bettor's record, the null hypothesis (H0) typically states that:

A) The bettor is skilled and has a genuine edge B) The bettor's win rate is equal to the breakeven rate C) The bettor has no predictive ability and results are due to chance D) The bettor's results are statistically significant

Question 2

A p-value of 0.03 means:

A) There is a 3% chance the null hypothesis is true B) There is a 3% chance the bettor has no skill C) If the null hypothesis were true, there is a 3% probability of observing results as extreme or more extreme than what was observed D) The bettor has a 97% chance of being skilled

Question 3

A Type I error in sports betting hypothesis testing occurs when:

A) You conclude a bettor is skilled when they actually are skilled B) You conclude a bettor is not skilled when they actually are skilled C) You conclude a bettor is skilled when they actually have no edge D) You fail to collect enough data to make a conclusion

Question 4

A bettor has won 270 out of 500 bets (54%). Under the null hypothesis of p = 0.50, what is the approximate standard error of the sample proportion?

A) 0.0100 B) 0.0224 C) 0.0500 D) 0.1000

Question 5

Which of the following sample sizes would typically be sufficient to detect a 53% true win rate as statistically significant (at alpha = 0.05 with 80% power) against a null of 50%?

A) 200 bets B) 500 bets C) 1,000 bets D) 3,000 bets

Question 6

The Bonferroni correction adjusts the significance level by:

A) Multiplying the p-values by the number of tests B) Dividing the significance level by the number of tests C) Taking the square root of the significance level D) Both A and B are equivalent valid descriptions

Question 7

A researcher tests 20 different betting strategies at the 5% significance level. If none of the strategies have a real edge, approximately how many would you expect to appear significant by chance?

A) 0 B) 1 C) 5 D) 10

Question 8

Statistical power is defined as:

A) The probability of rejecting H0 when H0 is true B) The probability of failing to reject H0 when H0 is false C) The probability of rejecting H0 when H0 is false D) The probability of failing to reject H0 when H0 is true

Question 9

A bettor has a 95% confidence interval for their win rate of [0.505, 0.575]. Which of the following is a correct interpretation?

A) There is a 95% probability their true win rate falls in this interval B) If they repeated their betting many times and constructed CIs each time, 95% of those intervals would contain the true win rate C) 95% of their future bets will fall within this range D) They are 95% confident they are a winning bettor

Question 10

The breakeven win rate for bets at -110 odds is approximately:

A) 50.0% B) 51.2% C) 52.4% D) 54.5%

Question 11

In a chi-squared goodness-of-fit test comparing observed versus expected betting outcomes across 6 categories, the degrees of freedom are:

A) 5 B) 6 C) 7 D) 12

Question 12

Which multiple testing correction method controls the False Discovery Rate (FDR) rather than the family-wise error rate (FWER)?

A) Bonferroni correction B) Holm-Bonferroni procedure C) Benjamini-Hochberg procedure D) Sidak correction

Question 13

A bettor checks their p-value after every 50 bets and stops as soon as they achieve p < 0.05. This practice:

A) Is a valid approach to sequential testing B) Inflates the Type I error rate above 0.05 C) Deflates the Type I error rate below 0.05 D) Has no effect on the Type I error rate

Question 14

Which of the following increases the power of a hypothesis test? (Select all that apply)

A) Increasing the sample size B) Increasing the significance level (alpha) C) The true effect size being larger D) All of the above

Question 15

A bettor has a record of 520 wins out of 1000 bets. The z-statistic for testing H0: p = 0.50 is:

A) 0.63 B) 1.26 C) 1.96 D) 2.53

Question 16

The "file drawer problem" in sports betting research refers to:

A) Researchers losing their data B) Studies with non-significant results not being published, creating a biased literature C) Bettors hiding their losing records D) Sportsbooks keeping their algorithms secret

Question 17

For a one-sided test at alpha = 0.05, the critical z-value is approximately:

A) 1.28 B) 1.645 C) 1.96 D) 2.33

Question 18

A Bayesian approach to evaluating a bettor differs from a frequentist approach primarily because:

A) It uses larger sample sizes B) It incorporates prior beliefs about the bettor's skill C) It always gives more significant results D) It does not require any data

Question 19

Two bettors each have a 55% win rate. Bettor A has 200 bets and Bettor B has 2000 bets. Which statement is most accurate?

A) Both provide equally strong evidence of skill B) Bettor A provides stronger evidence because the same win rate with fewer bets is more impressive C) Bettor B provides stronger evidence because the larger sample gives more precise estimation D) Neither provides strong evidence because 55% is barely above 50%

Question 20

When comparing the win rates of two independent groups (e.g., home favorites vs. road favorites), the appropriate test is:

A) Paired t-test B) One-sample z-test for proportions C) Two-sample z-test for proportions D) Chi-squared test for independence

Question 21

The Wilson score interval is preferred over the Wald interval for proportions because:

A) It is always narrower B) It has better coverage properties, especially for small samples or proportions near 0 or 1 C) It is easier to calculate D) It does not require any assumptions

Question 22

If a bettor needs 2,000 bets to demonstrate significance for a 53% true win rate, and they place 5 bets per week, approximately how long will it take?

A) About 2 years B) About 4 years C) About 7.5 years D) About 10 years

Question 23

The effect size in a test of betting skill is best described as:

A) The p-value B) The difference between the observed win rate and the null hypothesis win rate C) The sample size D) The confidence level

Question 24

When a sportsbook identifies a bettor as "sharp," they are essentially:

A) Committing a Type I error B) Rejecting the null hypothesis that the bettor has no edge C) Accepting the null hypothesis D) Performing a Bayesian analysis

Question 25

A researcher finds a p-value of 0.001 for a betting system that yields 50.5% wins over 100,000 games. The best interpretation is:

A) This is strong evidence of a profitable betting system B) This is strong evidence that the win rate differs from 50%, but the practical significance (effect size) is too small to be exploitable after vig C) The test must be incorrect because 50.5% is too close to 50% D) The researcher should use a smaller sample to get a more meaningful result

Answer Key

End of Chapter 8 Quiz