If the null hypothesis is true it should not be rejected Type I errors are also

# If the null hypothesis is true it should not be

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Consider a jury in a trial. The jury hears a sample of the information or evidence in the case. The jury assumes the defendant is innocent as the evidence is presented. Then, the jury determines if the defendant is guilty or not guilty based on the sample of evidence. The jury does not have every detail of the crime, but still have to determine the outcome of the case. An incorrect decision could send an innocent person to prison or set a guilty person free. In hypothesis testing, the same type of errors can occur. The null may be retained when it is false, or the null may be rejected when it is true. These errors are referred to as Type I and Type II errors.H0 True H0 False Reject the null Error: Type I Correct Decision Do not reject the null Correct Decision Error: Type IIWhen a true hypothesis is rejected, it is a type I error. A type I error is also known as a false positive. A false positive is a conclusion that there is a difference in a population that does not exist. If a researcher does not reject a false hypothesis, a type II error occurs. The type II error is also known as a false negative. The conclusion is no difference in the sample, but there is a difference.Both types of errors have negative consequences. Consider a type I error in a test for cancer. A false positive or type I error would be if the test indicated a person has cancer, when in reality, the person does not. For a type II error or false negative, the test results would indicate the person does not have cancer, but the person does. The level of significance relates to a type I error. The level of significance is the maximum probability of rejecting the null hypothesis when it is true. α = P(type I error). At α= 0.01, there is a 1% chance of a type I error or a 99% chance that a type I error will not be made. The probability of a type II error is represented by β, but is influenced by too many factors to analyze.Interactive Examples1When α= 0.01, there is a 1% chance of a type I error.2The average salary was reported as \$43,000 as the null was not rejected. However, the average
salary is actually \$41,000. What error was made?2When there is a 5% chance of a Type I error, what is the level of significance in the hypothesis test?3Given the null: The average life expectancy for a patient is 3 months or less. What is a Type II error?