Final answer:
In hypothesis testing for the dealer's win rate in blackjack, a z-test for proportions is used to compare the observed win rate against the claimed rate, with the 0.01 level of significance indicating a high threshold for rejecting the null hypothesis.
Step-by-step explanation:
Hypothesis Testing Using Sample Data
To evaluate the blackjack strategy book's claim about the dealer winning more than 52.5% of hands dealt, we use hypothesis testing. Given that a player recorded only 58 wins out of 100 hands for the dealer, we want to determine if this supports or refutes the author's claim. The 0.01 level of significance (1% risk of type I error) indicates a high level of stringent criteria against the null hypothesis.
Our null hypothesis (H0) is that the dealer wins at most 52.5% of the time, and the alternative hypothesis (H1) is that the dealer wins more than 52.5% of the time. We use a one-sample z-test for proportions to determine if the observed proportion of dealer wins, 58%, is significantly higher than the claimed proportion of 52.5%.
To perform this test, we calculate the z-value which is the number of standard deviations the sample proportion is from the hypothesized proportion, considering the binomial distribution of the win/loss record. We can then compare this z-value to the critical value associated with our chosen significance level by looking at standard statistical tables or using statistical software. If the z-value is greater than the critical value, we reject the null hypothesis.
An important note is that since this test is based on a sample of only 100 hands, the results may not conclusively represent the true win rate in a larger sample or in actual casino play. Further sampling and testing would be recommended for more robust conclusions.