A doctor is performing a clinical trial of a research medication for easing symptoms of emphysema. She recruits 50 patients with the disease and randomly assigns 25 to the treatment group and 25 to the placebo group. After 6 weeks, she measures each patient’s blood oxygen level and compares the sample means of the two groups. She calculates a test statistic of 4.38 and a p-value of 0.0001. She concludes that, since 0.0001 < 0.05, the medication significantly raises blood oxygen levels compared to the placebo. She calculates that the power of her test is 0.7.
What would constitute a type-I error in this scenario and what is its probability? What would constitute a type-II error in this scenario and what is its probability?
Type I error is rejection of null hypothesis given that the null hypothesis is true. In this scenario, type I error is the conclusion of the medication significantly raises blood oxygen levels compared to the placebo but in reality there is no difference in blood oxygen levels in patients treated with medications and placebo.
Probability of type I error is the significance level = 0.05
Type II error is failure to reject null hypothesis given that the null hypothesis is false. In this scenario, type II error is the conclusion of the medication does not significantly raises blood oxygen levels compared to the placebo but in reality there is significant difference in blood oxygen levels in patients treated with medications and placebo and the medication is effective in increasing the blood oxygen levels
Probability of type II error is the significance level = 1 - power = 1 - 0.7 = 0.3
A doctor is performing a clinical trial of a research medication for easing symptoms of emphysema....
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