Final answer:
The statement is false; the p-value is not chosen before a hypothesis test but is calculated from the data to evaluate the evidence against the null hypothesis. The level of significance (typically α) is what is chosen beforehand, which represents the researcher’s threshold for deciding whether to reject the null hypothesis.
Step-by-step explanation:
The statement that the p-value, which is the type I error rate, is chosen by the investigator before a hypothesis test is conducted is false. The p-value is actually a metric used to evaluate the evidence against a null hypothesis given the data observed in the study. It represents the probability that an event will happen purely by chance assuming the null hypothesis is true; the smaller the p-value, the stronger the evidence is against the null hypothesis.
In hypothesis testing, these definitions are crucial:
- A. An appropriate null hypothesis is usually a statement of no effect or no difference, and it is denoted as H0.
- B. An appropriate alternative hypothesis is a statement that indicates the presence of the effect or difference we're testing for, denoted as Ha or H1.
- C. The random variable, P', generally represents the calculated proportion or mean from the sample data used when testing a proportion or mean.
- D. Calculate the test statistic, which is a ratio that compares the difference between the observed sample statistic and the null hypothesis to the standard error of the sample statistic.
- E. The p-value is calculated based on the test statistic and tells us how likely the observed result is under the assumption that the null hypothesis is true.
- F. At the 5 percent level of decision, if the p-value is less than 0.05, the decision is to reject the null hypothesis.
- G. A Type I error is the incorrect rejection of a true null hypothesis.
- H. A Type II error occurs when the null hypothesis is not rejected, but it is actually false.
The level of significance, denoted by \(\alpha\), is indeed preset and represents the probability of making a Type I error. In contrast, the p-value is determined from the data and is not set in advance.