Final answer:
In hypothesis testing for comparing the "Both-Eye" and "Left-Eye" shooting methods, the Type II error rate (β) is related to the test's power and is not directly calculable from the given information. The Type I error rate (α) is 1% due to the significance level. A 95% confidence interval for the mean difference would require calculating the mean and standard deviation of the differences, then using the t-distribution for the interval.
Step-by-step explanation:
To investigate whether the "Both-Eye" method is different from the "Left-Eye" method for mean shooting accuracy for beginning shooters, we will utilize hypothesis testing. Assuming the shooting scores are normally distributed, and using a 1% significance level, we seek to answer the following questions:
A) The chance that we won't conclude a difference when there actually is one is known as the Type II error (or β). This value is not directly given but is related to the power of the test. The power of the test is the probability of correctly rejecting the null hypothesis when it is false, and it depends on the effect size, sample size, and significance level.
B) The chance that we will conclude a difference by mistake is known as the Type I error (or α), which in this case is 1% given the significance level.
H) To give a 95% confidence interval (CI) for the mean difference (Both - Left) for the population, we would calculate the mean and standard deviation of the differences and then apply the formula for the 95% CI, which involves the mean difference, standard deviation, and the critical value from the t-distribution since the population standard deviations are unknown.